Translating Word Phrases into Algebraic Equations Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

Which of the following algebraic expressions correctly represents the statement: 'Five less than the quotient of twice a number $p$ and three is subtracted from the product of four and the sum of the number and six'?

4(p + 6) - \left(\frac{2p}{3} - 5\right)

\left(\frac{2p}{3} - 5\right) - 4(p + 6)

4(p + 6) - \left(5 - \frac{2p}{3}\right)

4p + 6 - \left(\frac{2p}{3} - 5\right)

Show answer & explanation

Answer: $4(p + 6) - \left(\frac{2p}{3} - 5\right)$

Answer

The expression

4(p + 6) - \left(\frac{2p}{3} - 5\right)

correctly translates the word phrase into algebra.

The phrase requires breaking down into two parts. 'Five less than the quotient of twice a number

p

and three' translates to

(\frac{2p}{3} - 5)

because 'less than' reverses the order. 'The product of four and the sum of the number and six' translates to

4(p + 6)

because parentheses are needed to multiply the entire sum. Finally, 'is subtracted from' is a turnaround phrase meaning the first part is taken away from the second part, resulting in

4(p + 6) - \left(\frac{2p}{3} - 5\right)

.

Step-by-Step Solution

1

Translate the first phrase: 'Five less than the quotient of twice a number

p

and three'.

\frac{2p}{3} - 5

'Twice a number' is

2p

. The 'quotient... and three' means divide by

3

, giving

\frac{2p}{3}

. 'Five less than' indicates subtracting

5

from that quantity.

2

Translate the second phrase: 'the product of four and the sum of the number and six'.

4(p + 6)

'The sum of the number and six' requires grouping symbols:

(p + 6)

. 'The product of four and...' means multiplying

4

by the entire grouped sum.

3

Combine the two expressions using the operation 'is subtracted from'.

4(p + 6) - \left(\frac{2p}{3} - 5\right)

The phrase 'A is subtracted from B' translates to

B - A

. Therefore, the first expression must be subtracted from the second expression, requiring parentheses around the first expression.

Key Concept

Translating complex word phrases into algebraic expressions using correct order and grouping symbols.

Question 2Question →

Match each complex verbal phrase with its correct algebraic expression representation.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings match each complex verbal description with its respective mathematical translation: 'Twice the difference...' pairs with

2(3x - 7)

; 'Three times a number...' pairs with

(x + 5)^2 - 3x

; 'The quotient of...' pairs with

\frac{2x - 5}{x + 3}

; and 'The sum of...' pairs with

\frac{x + 4}{3x} - 8

.

Each verbal phrase contains specific operational keywords ('quotient', 'product', 'sum', 'difference') and ordering phrases ('subtracted from', 'less than'). Correct translation requires accurately identifying the operations, maintaining the proper sequence, and utilizing grouping symbols where compound expressions are modified.

Step-by-Step Solution

1

Analyze the first phrase: 'Twice the difference when seven is subtracted from three times a number

x

'.

The phrase translates to

2(3x - 7)

.

The phrase 'subtracted from' reverses the order, making it

3x - 7

. 'Twice the difference' requires multiplying the entire grouping by 2.

2

Analyze the second phrase: 'Three times a number

x

subtracted from the square of five more than the number'.

The phrase translates to

(x + 5)^2 - 3x

.

The base quantity is 'five more than the number' (

x + 5

), which is then squared to become

(x + 5)^2

. Subtracting

3x

from this quantity gives the final expression.

3

Analyze the third phrase: 'The quotient of five less than twice a number

x

and three more than the number'.

The phrase translates to

\frac{2x - 5}{x + 3}

.

'Quotient' implies a division. The first part, 'five less than twice a number', forms the numerator (

2x - 5

). The second part, 'three more than the number', forms the denominator (

x + 3

).

4

Analyze the fourth phrase: 'The sum of a number

x

and four, divided by the product of three and the number, all decreased by eight'.

The phrase translates to

\frac{x + 4}{3x} - 8

.

The fraction is constructed with 'the sum' (

x + 4

) over 'the product' (

3x

). The phrase 'all decreased by eight' instructs to subtract 8 from the complete fraction.

Key Concept

Accurately identifying operational keywords and recognizing the correct order of translation for phrases like 'less than' and 'subtracted from'.

Estimated Time:2m 0s

Question 3Question →

Which of the following equations correctly represents the statement: 'Twelve subtracted from five times the sum of a number $y$ and six is equal to three less than twice the number'?

5(y + 6) - 12 = 2y - 3

12 - 5(y + 6) = 3 - 2y

5y + 6 - 12 = 2y - 3

5(y + 6) - 12 = 3 - 2y

Show answer & explanation

Answer: $5(y + 6) - 12 = 2y - 3$

Answer

The equation

5(y + 6) - 12 = 2y - 3

correctly translates all verbal phrases in the appropriate order with necessary grouping symbols.

The translation process requires breaking the sentence into smaller chunks. The left side starts with 'five times the sum of a number

y

and six', written as

5(y + 6)

. Then, 'twelve subtracted from' means we subtract

12

from that product, yielding

5(y + 6) - 12

. The right side is 'three less than twice the number'. Twice the number is

2y

, and three less than that is

2y - 3

. Setting them equal gives

5(y + 6) - 12 = 2y - 3

.

Step-by-Step Solution

1

Translate 'the sum of a number

y

and six'.

(y + 6)

The word 'sum' indicates addition, and because this entire expression will be multiplied in the next step, it must be enclosed in parentheses.

2

Translate 'five times the sum'.

5(y + 6)

The multiplier

5

must apply to the entire grouped quantity of the sum.

3

Translate 'Twelve subtracted from' the previous result.

5(y + 6) - 12

The phrase 'subtracted from' means

12

is taken away from the established quantity, so it is placed after the minus sign.

4

Translate 'three less than twice the number'.

2y - 3

First, 'twice the number' is

2y

. 'Three less than' means

3

is subtracted from

2y

. This forms the right side of the equation.

Key Concept

Translating complex algebraic phrases requires careful attention to grouping words like 'sum' or 'difference' and order-reversing phrases like 'less than' or 'subtracted from'.

Question 4Question →

A word problem describes a quantity as being 'ten less than three times a number, $x$ '. What is the correct algebraic expression for this quantity?

3x - 10

10 - 3x

3(x - 10)

3x + 10

Show answer & explanation

Answer: $3x - 10$

Answer

The correct mathematical expression is

3x - 10

.

The phrase 'three times a number,

x

' translates directly to

3x

. The phrase 'ten less than' indicates a subtraction of

10

from that initial quantity. Therefore, the correct combined expression is

3x - 10

.

Step-by-Step Solution

1

Translate the multiplication part of the phrase: 'three times a number,

x

'.

3x

The word 'times' indicates multiplication between

3

and the variable

x

.

2

Translate the subtraction part of the phrase: 'ten less than'.

Subtract

10

from the result of step 1.

The phrase 'less than' is a turnaround phrase, meaning the value that comes before 'less than' must be subtracted from the value that comes after it.

3

Combine the translated parts into a single expression.

3x - 10

This correctly places the subtraction after the multiplied term.

Key Concept

Translating Word Phrases into Algebraic Equations

Question 5Question →

Match each verbal phrase with its correct algebraic expression translation.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The phrases correctly match with their algebraic translations based on the operational keywords: 'more than' maps to addition (

y + 4

), 'less than' maps to subtraction (

y - 4

), 'product' maps to multiplication (

4y

), and 'quotient' maps to division (

\frac{y}{4}

).

Matching each phrase requires identifying the key operation word: 'more than' for addition, 'less than' for subtraction (with reversed order), 'product' for multiplication, and 'quotient' for division. Applying these directly to the variable

y

and the number 4 yields the correct algebraic expressions.

Step-by-Step Solution

1

Translate 'Four more than a number

y

'.

y + 4

The words 'more than' specify adding to the given variable.

2

Translate 'Four less than a number

y

'.

y - 4

The words 'less than' specify subtracting from the given variable.

3

Translate 'The product of four and a number

y

'.

4y

The word 'product' specifies multiplying the values.

4

Translate 'The quotient of a number

y

and four'.

\frac{y}{4}

The word 'quotient' specifies dividing the first value by the second value.

Key Concept

Translating basic arithmetic operation keywords into their corresponding algebraic symbols.

Question 6Question →

A technician is configuring a power supply. The required output is described as twice the difference between the baseline voltage, $v$ , and six. What expression represents the required output?

2(v - 6)

2v - 6

2(6 - v)

6 - 2v

Show answer & explanation

Answer: $2(v - 6)$

Answer

The expression

2(v - 6)

correctly represents the required output.

The phrase 'difference between the baseline voltage,

v

, and six' translates to

(v - 6)

. The word 'twice' means multiplying this entire difference by

2

. Therefore, the correct translation must use parentheses to apply the multiplication to the whole difference, resulting in

2(v - 6)

.

Step-by-Step Solution

1

Translate 'the difference between the baseline voltage, v, and six'.

The expression becomes

v - 6

.

The word 'difference' indicates subtraction in the order the terms are given.

2

Translate 'twice' applied to the entire difference.

The expression becomes

2(v - 6)

.

Multiplying an entire binomial expression requires placing it in parentheses to ensure the multiplication applies to both terms.

Key Concept

Translating Word Phrases into Algebraic Equations

Question 7Question →

A shipment contains a number of crates equal to twice the quantity of seven less than the target value, $v$ . What expression defines the number of crates?

2(v - 7)

2v - 7

2(7 - v)

7 - 2v

Show answer & explanation

Answer: $2(v - 7)$

Answer

The correct expression is

2(v - 7)

.

The phrase 'seven less than the target value,

v

' establishes a baseline amount of

v - 7

. The problem then states we need 'twice the quantity of' that baseline amount. To multiply the entire baseline amount by two, we must enclose

v - 7

in parentheses, resulting in

2(v - 7)

.

Step-by-Step Solution

1

Translate the phrase 'seven less than the target value,

v

'.

The expression becomes

v - 7

.

The phrase 'less than' is a turnaround phrase, meaning the seven must be subtracted from the variable

v

.

2

Translate the phrase 'twice the quantity of' and apply it to the first step.

The final expression is

2(v - 7)

.

The word 'quantity' indicates that the entire previous expression (

v - 7

) must be grouped in parentheses before multiplying by two.

Key Concept

Translating Word Phrases into Algebraic Equations

Question 8Question →

Complete the algebraic equation that accurately translates the given statement.

Fill in the blanks below

Statement: 'Five subtracted from four times a number

k

equals eleven.'

Equation: - = 11

Show answer & explanation

Answer

The first blank is '4k' and the second blank is '5', forming the correct equation 4k - 5 = 11.

The phrase 'four times a number

k

' becomes

4k

. The phrase 'Five subtracted from' means 5 is taken away from

4k

, so the 5 must be placed after the minus sign, forming

4k - 5

. Finally, 'equals eleven' sets the expression equal to 11. Therefore, to match the provided equation structure of '___ - ___ = 11', the first blank must be filled with '4k' and the second blank must be filled with '5'.

Step-by-Step Solution

1

Translate the multiplication part of the statement.

'four times a number

k

' translates to the algebraic expression

4k

.

The word 'times' indicates multiplication between the coefficient 4 and the variable

k

.

2

Apply the subtraction part of the statement.

'Five subtracted from' means 5 is taken away from the previous term, resulting in

4k - 5

.

The phrase 'subtracted from' is a turnaround phrase, which means the 5 must be placed after the minus sign, reversing the spoken order.

3

Complete the equation.

Setting the expression equal to 11 gives the full equation:

4k - 5 = 11

.

The word 'equals' indicates where the equal sign (=) should be placed in relation to the constant 11.

Key Concept

Translating turnaround words (like 'subtracted from' or 'less than') and basic multiplication phrases into an algebraic equation.

Estimated Time:30s

Question 9Question →

An aircraft's current cruising altitude is $a$ feet. The required altitude for a new training maneuver is defined as four hundred feet less than triple the sum of the current altitude and two thousand. Which of the following algebraic expressions represents the required altitude in feet?

3(a + 2000) - 400

400 - 3(a + 2000)

3a + 2000 - 400

3(2000a) - 400

Show answer & explanation

Answer: $3(a + 2000) - 400$

Answer

The correct expression is

3(a + 2000) - 400

.

The correct answer accurately models the sequence of operations described in the text. It uses parentheses to group the addition

(a + 2000)

, multiplies that entire group by 3, and places the subtraction of 400 at the end of the expression to correctly satisfy the 'less than' condition.

Step-by-Step Solution

1

Translate 'the sum of the current altitude and two thousand'.

(a + 2000)

The word 'sum' indicates addition between the variable

a

and the number 2000. Parentheses are required because subsequent operations apply to this entire result.

2

Apply the multiplier 'triple' to the sum.

3(a + 2000)

'Triple' means multiplying the entire grouped quantity by 3.

3

Incorporate the phrase 'four hundred feet less than'.

3(a + 2000) - 400

The phrase 'less than' is a turnaround phrase, meaning the 400 must be subtracted from the previously established quantity.

Key Concept

Translating multi-step verbal phrases into algebraic expressions requires careful attention to grouping symbols and translation order, particularly for subtraction.

Question 10Question →

Match each verbal phrase or word problem to its correct algebraic equation translation.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches pair each verbal description with its mathematically equivalent equation by carefully translating order of operations, rates, geometric formulas, and grouping words.

Each verbal phrase uniquely defines a single algebraic relationship. By identifying key terms such as 'less than' for reverse-order subtraction, rate contexts for variable multiplication, geometric formulas for perimeter, and grouping words for parentheses, each scenario is mapped accurately to its corresponding equation.

Step-by-Step Solution

1

Analyze the first phrase: 'Eight less than five times a number

x

is equal to twenty.'

Translates to

5x - 8 = 20

.

'Five times a number' is

5x

. The phrase 'less than' dictates that 8 is subtracted from

5x

.

2

Analyze the second phrase: 'A service charges 8 dollars per hour plus a 5 dollar flat fee. The total cost for

x

hours is 20 dollars.'

Translates to

8x + 5 = 20

.

The variable

x

is multiplied by the hourly rate of 8, and the one-time flat fee of 5 is added to this product.

3

Analyze the third phrase: 'The perimeter of a rectangle is 20. Its length is 5 units more than its width,

x

.'

Translates to

2x + 2(x + 5) = 20

.

The perimeter formula is

2W + 2L

. Substituting

x

for width and

(x + 5)

for length provides the correct equation.

4

Analyze the fourth phrase: 'Five times the difference of a number

x

and eight results in twenty.'

Translates to

5(x - 8) = 20

.

The word 'difference' combined with 'times' indicates that the subtraction

(x - 8)

must occur first, requiring parentheses before multiplying by 5.

Key Concept

Translating complex word phrases into algebraic equations requires strict attention to operation order, grouping symbols, and contextual formulas.

Question 11Question →

Translate the following verbal statement into algebraic expressions representing each side of the equation:

'Eleven less than three times a number, $q$ , is equal to five times the sum of the number and two.'

Fill in the blanks below

The expression for 'Eleven less than three times a number,

q

' is:

The expression for 'five times the sum of the number and two' is:

Show answer & explanation

Answer

The left expression is 3q - 11 and the right expression is 5(q + 2).

The verbal phrase 'less than' requires the subtracted amount to follow the term it modifies, making the first expression 3q - 11. The phrase 'times the sum of' explicitly requires multiplying by a grouped addition, making the second expression 5(q + 2).

Step-by-Step Solution

1

Translate the phrase representing the left side of the equation: 'Eleven less than three times a number,

q

'.

3q - 11

The phrase 'three times a number,

q

' translates directly to 3q. The phrase 'less than' dictates that 11 is subtracted from 3q, reversing the apparent reading order of the words.

2

Translate the phrase representing the right side of the equation: 'five times the sum of the number and two'.

5(q + 2)

The phrase 'sum of the number and two' translates to (q + 2). Grouping symbols (parentheses) are required because the multiplication by five applies to the entire sum, not just the first term.

Key Concept

Translating complex algebraic phrases by correctly applying order-reversing terminology and grouping indicators.

Estimated Time:1m 0s

Question 12Question →

A structural engineer calculates the maximum safe load, $L$ , for a support beam. The safe load is equal to fifty less than triple the sum of the beam's cross-sectional area, $A$ , and twelve. What algebraic equation models the maximum safe load?

L = 3(A + 12) - 50

L = 50 - 3(A + 12)

L = 3A + 12 - 50

L = 3(A + 12) + 50

Show answer & explanation

Answer: $L = 3(A + 12) - 50$

Answer

The correct equation is

L = 3(A + 12) - 50

.

The correct equation methodically translates the text: 'the sum of... A, and twelve' becomes the grouped quantity (A + 12). 'Triple' multiplies this entire group by 3, giving 3(A + 12). Finally, 'fifty less than' dictates subtracting 50 from that product, yielding 3(A + 12) - 50.

Step-by-Step Solution

1

Identify the base quantity being modified.

The phrase 'the sum of the beam's cross-sectional area,

A

, and twelve' translates algebraically to the grouped expression

(A + 12)

.

The word 'sum' implies addition, and it creates a single quantity that must be grouped in parentheses before further operations are applied.

2

Translate the multiplier.

The word 'triple' indicates multiplication by 3, resulting in the expression

3(A + 12)

.

The multiplier applies to the entire sum identified in the previous step.

3

Translate the subtraction phrase.

The phrase 'fifty less than' means subtracting 50 from the previously established quantity, yielding

3(A + 12) - 50

.

In algebraic translation, 'X less than Y' dictates an order reversal to become Y - X.

4

Form the final equation.

Set the maximum safe load,

L

, equal to the derived expression:

L = 3(A + 12) - 50

.

The problem states that the safe load is equal to the verbal expression.

Key Concept

Translating order-dependent phrases and implied grouping symbols from English into algebraic notation.

Estimated Time:45s

Question 13Question →

A customer's monthly utility bill is calculated as twelve dollars less than three times the sum of their base usage fee, $f$ , and five. If the total bill amounts to $108$ , which of the following equations correctly models this calculation?

3(f + 5) - 12 = 108

12 - 3(f + 5) = 108

3f + 5 - 12 = 108

3(5f) - 12 = 108

Show answer & explanation

Answer: $3(f + 5) - 12 = 108$

Answer

The equation that correctly represents the calculation is

3(f + 5) - 12 = 108

.

The equation is built step-by-step: 'the sum of their base usage fee,

f

, and five' is written as

(f + 5)

. 'Three times' this sum requires multiplying the grouped expression, resulting in

3(f + 5)

. Finally, 'twelve dollars less than' means

12

must be subtracted from that product, yielding the final correct equation

3(f + 5) - 12 = 108

.

Step-by-Step Solution

1

Translate the phrase 'the sum of their base usage fee,

f

, and five'.

(f + 5)

The phrase 'the sum of' indicates addition between the variable

f

and the number

5

. Parentheses are required because a subsequent operation applies to this entire sum.

2

Translate 'three times the sum'.

3(f + 5)

The multiplier

3

must distribute across the entire sum, which is represented by placing it directly outside the parentheses.

3

Translate 'twelve dollars less than'.

3(f + 5) - 12

The phrase 'less than' is a turnaround phrase meaning

12

is subtracted from the quantity that precedes it conceptually, placing

- 12

at the end.

4

Form the complete equation by setting the expression equal to the total bill.

3(f + 5) - 12 = 108

The phrase 'amounts to' signifies equality with the final given value of

108

.

Key Concept

Translating complex word phrases into algebraic equations requires careful attention to operation order, turnaround words like 'less than', and grouping symbols for terms like 'the sum of'.

Estimated Time:1m 0s

Question 14Question →

Match each verbal phrase describing a mathematical relationship or scenario to its correct algebraic expression.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings match each contextual or mathematical description with its exact symbolic translation, respecting order of operations, geometric formulas, and grouping words.

Each correct match successfully identifies key translation words ('product', 'quotient', 'less than', 'quantity') and applies proper algebraic syntax, including necessary parentheses, geometric formulas, and the correct order for subtraction.

Step-by-Step Solution

1

Translate the rate and discount scenario.

The phrase '

k

items at twelve dollars each' translates to

12k

. The phrase 'minus a five-dollar discount' makes it

12k - 5

.

Multiplication represents a per-item rate, and a discount implies subtraction.

2

Translate the quotient phrase.

The 'quotient of

k

and five' is

\frac{k}{5}

. 'Twelve less than' means subtracting

12

from this term, yielding

\frac{k}{5} - 12

.

The phrase 'less than' dictates reversing the order of the terms in the algebraic subtraction.

3

Translate the grouped product phrase.

The 'quantity of five less than

k

' is translated as

(k - 5)

. The 'product of twelve and the quantity' is

12(k - 5)

.

The word 'quantity' signals that the addition or subtraction must be grouped in parentheses before applying the multiplication.

4

Translate the geometric scenario.

The 'area of a rectangle with length twelve and width

k

' translates to

12k

. 'Increased by five' adds

5

, yielding

12k + 5

.

Area of a rectangle is calculated by multiplying length and width, and 'increased by' signifies addition.

Key Concept

Translating Word Phrases into Algebraic Equations

Question 15Question →

The maximum payload capacity, $C$ , of a transport drone is equal to twice the sum of its base weight, $w$ , and fifty, subtracted from five hundred. Which of the following equations correctly models this capacity?

C = 500 - 2(w + 50)

C = 2(w + 50) - 500

C = 500 - 2w + 50

C = 2w + 50 - 500

Show answer & explanation

Answer: $C = 500 - 2(w + 50)$

Answer

The correct equation is

C = 500 - 2(w + 50)

.

The correct equation translates the text sequentially while respecting mathematical grouping. First, 'the sum of its base weight,

w

, and fifty' translates to the grouped expression

(w + 50)

. 'Twice the sum' means multiplying that entire group by 2, yielding

2(w + 50)

. Finally, 'subtracted from five hundred' dictates the order of the subtraction: 500 is the initial amount from which the expression is taken away, resulting in

500 - 2(w + 50)

.

Step-by-Step Solution

1

Translate the phrase 'the sum of its base weight, w, and fifty'.

(w + 50)

The word 'sum' indicates addition, and since it is a single combined quantity, it must be enclosed in parentheses.

2

Translate the phrase 'twice the sum'.

2(w + 50)

The word 'twice' means multiplying by 2. It applies to the entire sum.

3

Translate the phrase 'subtracted from five hundred' to form the final equation.

C = 500 - 2(w + 50)

The phrase 'subtracted from X' means X is the starting amount. Therefore, the expression

2(w + 50)

must be subtracted from 500.

Key Concept

Translating Word Phrases into Algebraic Equations

Question 16Question →

Read the scenario below and fill in the missing values to complete the corresponding algebraic equation.

A network administrator calculates the total required bandwidth, $B$ , as seventy-five less than quadruple the sum of the base traffic, $t$ , and twenty.

Fill in the blanks below

B =

(t +

) -

Show answer & explanation

Answer

The completed equation is

B = 4(t + 20) - 75

. Therefore, blank 1 is 4, blank 2 is 20, and blank 3 is 75.

The scenario requires piecing together three mathematical operations. First, 'the sum of the base traffic, t, and twenty' creates the grouped expression

(t + 20)

. Next, 'quadruple' means multiplying that entire sum by 4, resulting in

4(t + 20)

. Finally, 'seventy-five less than' indicates that 75 must be subtracted from that product. Putting it all together gives

4(t + 20) - 75

, which fits perfectly into the provided blanks as 4, 20, and 75.

Step-by-Step Solution

1

Identify the core grouped expression.

The phrase 'the sum of the base traffic, t, and twenty' translates to

(t + 20)

.

The word 'sum' indicates addition, and it groups the terms together.

2

Apply the multiplication factor.

The phrase 'quadruple the sum' translates to

4(t + 20)

.

The word 'quadruple' means to multiply a quantity by 4.

3

Apply the subtraction.

The phrase 'seventy-five less than' means subtracting 75 from the entire previous expression, yielding

4(t + 20) - 75

.

The phrase 'less than' is a turnaround phrase, meaning the value being subtracted goes at the end of the expression.

4

Map the components to the provided equation structure.

Comparing

4(t + 20) - 75

to the template

B =

blank_1

(t +

blank_2

) -

blank_3, we find blank_1 is 4, blank_2 is 20, and blank_3 is 75.

This completes the algebraic translation in the required format.

Key Concept

Translating verbal descriptions of arithmetic operations and their structural order into an algebraic equation.

Estimated Time:45s

Question 17Question →

In a manufacturing process, the required cooling time in minutes is defined as eight subtracted from twice the sum of the baseline time, $t$ , and four. Which of the following algebraic expressions represents the required cooling time?

2(t + 4) - 8

8 - 2(t + 4)

2t + 4 - 8

2(5t) - 8

Show answer & explanation

Answer: $2(t + 4) - 8$

Answer

The correct algebraic expression is

2(t + 4) - 8

.

The correct expression carefully follows the algebraic translation rules: 'sum' dictates the grouping

(t + 4)

, 'twice' multiplies that entire group by 2 to get

2(t + 4)

, and 'eight subtracted from' places the

- 8

at the end of the expression.

Step-by-Step Solution

1

Identify and group the addition operation described in the problem.

(t + 4)

The phrase 'the sum of the baseline time,

t

, and four' indicates that these two quantities must be added and kept together as a single unit.

2

Apply the multiplication to the grouped sum.

2(t + 4)

The word 'twice' means multiplying the entire group by 2.

3

Translate the subtraction phrase in the correct order.

2(t + 4) - 8

The phrase 'eight subtracted from' is a turnaround phrase, meaning 8 must be taken away from the grouped expression.

Key Concept

Translating complex word phrases requires identifying grouping words (like 'sum') to use parentheses, and recognizing turnaround phrases (like 'subtracted from') that reverse the written order in the mathematical expression.

Translating Word Phrases into Algebraic Equations

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes