Tüm alıştırma soruları

Soru 441Soru →

A military training field is rectangular, measuring $160$ yards wide and $300$ yards long. A recruit must travel from one corner of the field to the opposite corner. If the recruit runs directly across the diagonal instead of moving along the outer edges of the two sides, how many yards does the recruit save?

Cevabı ve açıklamayı göster

Cevap: 120

Cevap

120 yards

The route along the edges is the sum of the width and length (

160 + 300 = 460

yards). The diagonal route is the hypotenuse of the right triangle formed by these sides, calculated as

\sqrt{160^2 + 300^2} = 340

yards. The distance saved is

460 - 340 = 120

yards.

Adım Adım Çözüm

1

Calculate the total distance if traveling along the two outer edges of the rectangular field.

160 + 300 = 460

yards.

This establishes the longer route distance to compare against the diagonal shortcut.

2

Set up the Pythagorean theorem to find the length of the diagonal route.

160^2 + 300^2 = c^2

The rectangular field forms a right triangle where the width and length are the legs, and the diagonal is the hypotenuse.

3

Solve for the diagonal length (

c

).

c = \sqrt{115600} = 340

yards.

This gives the exact distance of the direct route.

4

Calculate the difference between the two routes.

460 - 340 = 120

yards.

Subtracting the shorter diagonal route from the longer perimeter route yields the exact distance saved.

Anahtar Kavram

Applying the Pythagorean theorem (

a^2 + b^2 = c^2

) to find a direct diagonal distance, and comparing it to the linear distance along the edges.

Soru 442Soru →

What is the exact value of the following mathematical expression?

\frac{10 - (-2)}{3} + 4^2

Cevabı ve açıklamayı göster

Cevap: 20

Cevap

The correct value is 20.

The expression is correctly evaluated by first simplifying the numerator grouping

10 - (-2)

to get

12

, dividing by

3

to obtain

4

, evaluating the exponent

4^2

to get

16

, and finally adding the results together to reach

20

.

Adım Adım Çözüm

1

Simplify the grouping symbol formed by the numerator.

10 - (-2) = 12

The numerator of a fraction acts as a grouping symbol and must be evaluated first.

2

Divide the simplified numerator by the denominator.

\frac{12}{3} = 4

The fraction bar represents division, which should be completed before addition.

3

Evaluate the exponent.

4^2 = 16

According to the order of operations, exponents must be evaluated before addition.

4

Add the remaining values.

4 + 16 = 20

Addition is the final operation left in the expression.

Anahtar Kavram

Order of Operations with fractions and signed numbers

Tahmini Süre:45s

Soru 443Soru →

A surveyor is mapping a plot of land and launches a drone from a perfectly flat field. The drone ascends vertically to an altitude of $30$ meters. It then travels horizontally in a straight line for $16$ meters to photograph a landmark. What is the direct line-of-sight distance, in meters, from the launch point on the ground to the drone?

Cevabı ve açıklamayı göster

Cevap: 34

Cevap

The direct line-of-sight distance is

34

meters.

The drone's flight path forms a right-angled triangle relative to the starting point. By applying the Pythagorean theorem (

a^2 + b^2 = c^2

), we square the vertical distance (

30^2 = 900

) and the horizontal distance (

16^2 = 256

). Adding these values yields

1156

. Taking the square root of

1156

gives the direct line-of-sight distance, which is

34

meters.

Adım Adım Çözüm

1

Model the drone's flight path as a right-angled triangle.

The vertical ascent forms one leg (

a = 30

) and the horizontal flight forms the other leg (

b = 16

). The direct line-of-sight distance is the hypotenuse (

c

).

Vertical and horizontal movements are perpendicular, creating a

90^\circ

angle.

2

Apply the Pythagorean theorem to calculate the hypotenuse.

a^2 + b^2 = c^2

becomes

30^2 + 16^2 = c^2

.

The Pythagorean theorem relates the lengths of the legs to the length of the hypotenuse in any right triangle.

3

Square the lengths of the two legs and add them together.

900 + 256 = 1156

. So,

c^2 = 1156

.

This evaluates the left side of the equation to isolate

c^2

.

4

Take the square root of the sum to find the actual distance.

c = \sqrt{1156} = 34

.

Taking the square root of

c^2

yields the length of the hypotenuse.

Anahtar Kavram

Applying the Pythagorean theorem to find the hypotenuse in a practical right-triangle scenario.

Soru 444Soru →

What is the exact numerical value of the following mathematical expression?

|-18| - 7^2 + \frac{45}{-9}

Cevabı ve açıklamayı göster

Cevap: -36

Cevap

The correct numerical value is -36.

To evaluate the expression, follow the order of operations strictly. First, resolve the absolute value: |-18| becomes 18. Next, evaluate the exponent: 7^2 becomes 49 (note that the negative sign is separate from the squared base). Then, perform the division: 45 divided by -9 equals -5. Finally, perform the remaining subtraction and addition from left to right: 18 - 49 equals -31, and -31 + (-5) yields the final answer of -36.

Adım Adım Çözüm

1

Evaluate the absolute value.

|-18| = 18

Absolute value acts as a grouping symbol and must be processed first, returning the non-negative distance from zero.

2

Evaluate the exponential term.

7^2 = 49

Exponents are evaluated before multiplication, division, addition, and subtraction. The negative sign is outside the base, so only the 7 is squared.

3

Evaluate the division.

\frac{45}{-9} = -5

Division and multiplication are evaluated before addition and subtraction.

4

Evaluate addition and subtraction from left to right.

18 - 49 + (-5) = -36

Addition and subtraction hold the same precedence and are solved strictly from left to right as they appear.

Anahtar Kavram

Order of Operations with signed numbers, absolute value, and exponents

Soru 445Soru →

A cosmetics laboratory prepares a bulk batch of hand sanitizer containing $3$ gallons and $2$ quarts. The sanitizer will be packaged into small travel bottles that hold $4$ fluid ounces each. How many travel bottles can be completely filled from this batch?

Cevabı ve açıklamayı göster

Cevap: 112

Cevap

112

The correct answer is found by first unifying the entire volume into fluid ounces. Converting the 3 gallons into quarts yields 12 quarts. Adding the extra 2 quarts brings the total to 14 quarts. Because there are 32 fluid ounces in a single quart, you multiply 14 by 32 to determine the batch contains 448 fluid ounces. Dividing this total by the 4-ounce capacity per bottle yields exactly 112 bottles.

Adım Adım Çözüm

1

Convert the gallons portion to quarts.

3 gallons = 12 quarts

Converting to a smaller common unit makes it easier to combine the total volume.

2

Find the total volume in quarts.

12 quarts + 2 quarts = 14 quarts

This gives the complete batch size in a single unit.

3

Convert the total quarts to fluid ounces.

14 quarts × 32 fluid ounces/quart = 448 fluid ounces

The bottles are measured in fluid ounces, so the total volume must match this unit before dividing.

4

Divide the total fluid ounces by the capacity of each bottle.

448 ÷ 4 = 112

This determines the exact number of travel bottles that can be filled.

Anahtar Kavram

Converting mixed US customary volume units (gallons and quarts) to fluid ounces and dividing by a unit rate.

Soru 446Soru →

Consider the mathematical expression below:

-4^2 - \frac{36 \div (-3) \times 2}{|1 - 4|}

What is the exact evaluated value of this expression?

Cevabı ve açıklamayı göster

Cevap: -8

Cevap

-8

The correct answer is derived by carefully following the order of operations (PEMDAS/BODMAS). First, the denominator's absolute value evaluates to 3. Second, evaluating the numerator strictly from left to right gives

36 \div (-3) = -12

, and

-12 \times 2 = -24

. The entire fraction therefore simplifies to

-24 \div 3 = -8

. Next, the exponent

-4^2

evaluates to

-16

because the negative sign is not inside parentheses. Finally, subtracting the fraction's value yields

-16 - (-8)

, which simplifies to

-16 + 8 = -8

.

Adım Adım Çözüm

1

Evaluate the absolute value grouping in the denominator.

|1 - 4| = |-3| = 3

Absolute value bars act as grouping symbols and must be evaluated first. Absolute value always returns a non-negative distance.

2

Evaluate the numerator from left to right.

36 \div (-3) \times 2 = -12 \times 2 = -24

Multiplication and division have equal precedence, so they must be evaluated strictly from left to right.

3

Simplify the fraction by dividing the numerator by the denominator.

\frac{-24}{3} = -8

The fraction bar acts as a grouping symbol separating the numerator and denominator.

4

Evaluate the exponent term.

-4^2 = -16

Without parentheses around the base, the exponent applies only to the 4, not the negative sign.

5

Perform the final subtraction.

-16 - (-8) = -16 + 8 = -8

Subtracting a negative number is equivalent to adding its positive value.

Anahtar Kavram

Applying the order of operations (PEMDAS), specifically evaluating multiplication/division from left to right, processing absolute values, and understanding how exponents apply to negative bases without parentheses.

Soru 447Soru →

A naval shipyard increases its dry dock maintenance workforce by $12.5\%$ to meet new project demands. If the current workforce size after the increase is $810$ personnel, what was the original size of the workforce before the increase?

Cevabı ve açıklamayı göster

Cevap: 720

Cevap

720

The scenario requires a reverse percentage calculation. The final count of

810

personnel represents the original workforce plus a

12.5\%

increase, meaning

810

is exactly

112.5\%

(or

\frac{9}{8}

) of the original amount. To find the original amount, you set up the equation

\frac{9}{8}x = 810

and solve for

x

by multiplying

810

by the reciprocal

\frac{8}{9}

, which equals

720

.

Adım Adım Çözüm

1

Identify the relationship between the final amount and the initial amount.

A

12.5\%

increase means the final amount is

100\% + 12.5\% = 112.5\%

of the original amount.

To correctly set up an algebraic representation of the percentage growth based on the unknown starting value.

2

Convert the new percentage multiplier into a fraction.

Knowing that

12.5\% = \frac{1}{8}

, the multiplier for a

12.5\%

increase is

1 + \frac{1}{8} = \frac{9}{8}

.

Using fractions makes mental arithmetic much simpler and faster without a calculator.

3

Set up the equation to solve for the original amount.

Letting

x

represent the original workforce size, the equation is

\frac{9}{8}x = 810

.

This translates the word problem into a solvable mathematical equation.

4

Solve the equation for

x

.

x = 810 \times \frac{8}{9} = 90 \times 8 = 720

.

Isolating

x

provides the initial workforce size before the increase.

Anahtar Kavram

Reverse percentage calculations and percentage-to-fraction conversions.

Tahmini Süre:1m 0s

Soru 448Soru →

A fuel tank at a military base is initially filled to $80\%$ of its total capacity. After a training exercise, the fuel level decreases by $35\%$ of its current volume. If $260$ gallons of fuel remain in the tank after the exercise, what is the total capacity of the fuel tank in gallons?

Cevabı ve açıklamayı göster

Cevap: 500

Cevap

500

To find the total capacity, we must track the percentage of fuel at each stage relative to the total capacity. Initially, the tank holds

80\%

of its capacity, or

0.80

. A decrease of

35\%

means

65\%

of that fuel remains. Multiplying the initial proportion (

0.80

) by the remaining proportion (

0.65

) yields

0.52

. This indicates that the final

260

gallons represent exactly

52\%

of the tank's total capacity. Setting up the equation

0.52C = 260

and dividing

260

by

0.52

gives a total capacity of

500

gallons.

Adım Adım Çözüm

1

Define a variable for the total capacity and express the initial fuel volume.

Initial volume =

0.80C

The tank is starting at

80\%

of its total capacity (

C

).

2

Determine the percentage of fuel remaining after the exercise.

Remaining percentage =

100\% - 35\% = 65\%

A

35\%

decrease means that

65\%

of the fuel that was in the tank before the exercise is still there.

3

Express the final remaining volume in terms of the total capacity (

C

).

0.65 \times 0.80C = 0.52C

Applying the

65\%

remaining proportion to the initial

0.80C

volume gives the final percentage of the total capacity.

4

Set up an equation using the known final volume and solve for

C

.

0.52C = 260 \Rightarrow C = \frac{260}{0.52} = 500

Equating the algebraic expression to the

260

gallons given in the problem isolates the unknown base capacity.

Anahtar Kavram

Calculating successive percentages and identifying an unknown base value.

Soru 449Soru →

During scheduled maintenance on the airfield Mobile Aircraft Arresting System (MAAS), technicians inspect the energy absorber brakes. The primary hydraulic retractor operates at an operating pressure of 1,850 PSI, while the brake accumulator must be pre-charged with dry nitrogen to 450 PSI. During routine proof-testing, the maximum allowable surge pressure is 2,200 PSI, and complete fluid replacement is mandated every 36 months.

According to the passage, what is the required dry nitrogen pre-charge pressure, in PSI, for the brake accumulator?

Cevabı ve açıklamayı göster

Cevap: 450

Cevap

450 PSI

The passage explicitly states that 'the brake accumulator must be pre-charged with dry nitrogen to 450 PSI.' Thus, 450 is the exact required value.

Adım Adım Çözüm

1

Scan the passage to locate the specific component and parameter in question.

Located the phrase: 'the brake accumulator must be pre-charged with dry nitrogen to 450 PSI.'

Isolating the target component ensures that the quantity extracted is not confused with adjacent technical specifications.

2

Extract the exact numerical figure associated with the accumulator pre-charge.

450 PSI

The passage directly links 450 PSI to the dry nitrogen pre-charge requirement for the accumulator.

Anahtar Kavram

Extracting specific numerical values linked to distinct technical components from an informational passage

Tahmini Süre:1m 0s

Soru 450Soru →

A maintenance squad has $250$ spark plugs in their inventory. After a week of vehicle repairs, the inventory is reduced by $40\%$ . How many spark plugs are left in the inventory?

Cevabı ve açıklamayı göster

Cevap: 150

Cevap

150

Since

40\%

of the inventory was used,

60\%

remains. Multiplying the original

250

spark plugs by

0.60

results in

150

spark plugs left.

Adım Adım Çözüm

1

Calculate the percentage of the inventory that remains.

100\% - 40\% = 60\%

The total starting inventory represents

100\%

. Subtracting the

40\%

reduction gives the percentage that is left.

2

Calculate

60\%

of the initial

250

spark plugs.

250 \times 0.60 = 150

Multiplying the initial amount by the decimal form of the remaining percentage gives the final quantity.

Anahtar Kavram

Calculating the remaining quantity after a percentage decrease.

Soru 451Soru →

What is the absolute difference between the smallest positive integer and the largest negative integer?

Cevabı ve açıklamayı göster

Cevap: 2

Cevap

2

The smallest positive integer is 1 and the largest negative integer is -1. The absolute difference between them is found by subtracting the two values and taking the absolute value:

|1 - (-1)| = |1 + 1| = 2

.

Adım Adım Çözüm

1

Identify the smallest positive integer.

1

The integer 0 is neither positive nor negative. The positive integers start at 1, making it the smallest positive integer.

2

Identify the largest negative integer.

-1

Negative integers increase in value as they get closer to zero. Therefore, -1 is the largest negative integer.

3

Calculate the absolute difference.

2

The absolute difference represents the total distance between the two numbers on the number line. Calculate this as

|1 - (-1)| = |1 + 1| = 2

.

Anahtar Kavram

Properties of Integers (Number Line and Absolute Value)

Soru 452Soru →

What is the greatest integer value of $x$ that satisfies the following inequality?

3(4 - 2x) - 2x > 5(x - 3) - 10x

Cevabı ve açıklamayı göster

Cevap: 8

Cevap

8

Solving the inequality yields x < 9. Since the inequality is strictly less than 9, the greatest integer that satisfies the condition is 8.

Adım Adım Çözüm

1

Distribute the 3 and 5

12 - 6x - 2x > 5x - 15 - 10x

To eliminate the parentheses on both sides of the inequality.

2

Combine like terms

12 - 8x > -5x - 15

To simplify both sides before isolating the variable.

3

Isolate the variable terms

-3x > -27

Subtract 12 from both sides and add 5x to both sides to get all x terms on the left and constants on the right.

4

Divide by -3

x < 9

Dividing an inequality by a negative number requires flipping the inequality sign.

5

Find the greatest integer

8

The inequality states x must be strictly less than 9, so the largest possible integer is 8.

Anahtar Kavram

Solving linear inequalities, applying the negative division flip rule, and interpreting integer boundaries.

Soru 453Soru →

What is the minimum integer value of

x

that satisfies the following inequality?

-3x + 2 \leq 14

Cevabı ve açıklamayı göster

Cevap: -4

Cevap

-4

By isolating the variable and correctly reversing the inequality sign when dividing by a negative number, we find the solution set is

x \geq -4

. The smallest integer in this set is -4.

Adım Adım Çözüm

1

Subtract 2 from both sides of the inequality.

-3x \leq 12

To isolate the variable term.

2

Divide both sides by -3 and reverse the inequality sign.

x \geq -4

Dividing an inequality by a negative number requires reversing the direction of the inequality symbol to maintain the true mathematical relationship.

3

Find the minimum integer value that satisfies the solution set.

-4

The solution set includes all numbers greater than or equal to -4. The smallest integer in this set is -4.

Anahtar Kavram

Solving two-step linear inequalities and applying the rule for dividing by a negative number.

Soru 454Soru →

An important part of algebraic evaluation is applying operations in the correct sequence. Consider the mathematical expression provided below:

-3^2 + 4 \times [15 \div (2 - 5)] - (-6)

What is the final calculated value of this expression?

Cevabı ve açıklamayı göster

Cevap: -23

Cevap

-23

Following the strict order of operations, we first resolve the grouping symbols from the inside out to get

-5

for the bracketed term. Next, we evaluate the isolated exponent

-3^2

as

-9

. Then, we multiply the

4

by our bracketed result of

-5

to get

-20

. Finally, we perform addition and subtraction from left to right:

-9 + (-20) + 6

, which results in

-23

.

Adım Adım Çözüm

1

Evaluate innermost parentheses

(2 - 5) = -3

Order of operations dictates solving expressions inside the innermost grouping symbols first.

2

Evaluate brackets

[15 \div (-3)] = -5

Continue evaluating operations inside the next level of grouping symbols.

3

Evaluate exponent

-3^2 = -9

Exponents are evaluated before multiplication and division. The negative sign is outside the base, so only the 3 is squared.

4

Perform multiplication

4 \times (-5) = -20

Multiplication and division are performed from left to right before any addition or subtraction.

5

Perform addition and subtraction

-9 + (-20) - (-6) = -23

Add and subtract from left to right. Subtracting a negative number is mathematically equivalent to adding a positive number.

Anahtar Kavram

Applying the order of operations (PEMDAS) to expressions with nested grouping symbols, exponents, and signed numbers.

Soru 455Soru →

During a physical fitness assessment, $68$ recruits met the advanced standard. If these recruits represent $17\%$ of the total training company, what is the total number of recruits in the company?

Cevabı ve açıklamayı göster

Cevap: 400

Cevap

400

The correct total is found by recognizing the relationship:

\text{Part} = \text{Rate} \times \text{Base}

. We are given the Part (

68

) and the Rate (

17\%

or

0.17

). To find the Base, we divide the Part by the Rate:

68 \div 0.17 = 400

.

Adım Adım Çözüm

1

Set up an algebraic equation relating the given part to the unknown whole.

0.17 \times x = 68

The problem states that

17\%

of the total class (

x

) is equal to

68

recruits.

2

Isolate the variable

x

to solve for the total.

x = \frac{68}{0.17}

Dividing both sides of the equation by

0.17

will leave

x

by itself.

3

Perform the division without a calculator.

x = 400

Multiply the numerator and denominator by

100

to remove the decimal, resulting in

\frac{6800}{17}

. Since

17 \times 4 = 68

,

\frac{6800}{17}

equals

400

.

Anahtar Kavram

Finding the original base when a percentage rate and its corresponding amount are known.

Tahmini Süre:1m 0s

Soru 456Soru →

A military transport aircraft has a maximum cargo capacity of $15,000 \text{ kilograms}$ . The aircraft is currently loaded with $19,800 \text{ pounds}$ of equipment. If $1 \text{ kilogram}$ is equal to $2.2 \text{ pounds}$ , how much additional cargo, in kilograms, can the aircraft carry?

Cevabı ve açıklamayı göster

Cevap: 6000

Cevap

6000

The remaining capacity is found by first standardizing all measurements to kilograms (

19,800 \text{ pounds} \div 2.2 = 9,000 \text{ kilograms}

), and then subtracting this from the total allowance (

15,000 \text{ kg} - 9,000 \text{ kg} = 6,000 \text{ kg}

).

Adım Adım Çözüm

1

Convert the current load from pounds to kilograms.

19,800 \div 2.2 = 9,000 \text{ kg}

Since the maximum capacity is given in kilograms and the final answer must be in kilograms, the current load must be converted to the metric system.

2

Subtract the current load from the maximum cargo capacity.

15,000 - 9,000 = 6,000 \text{ kg}

Subtracting the weight already on board from the maximum allowable weight gives the remaining available capacity.

Anahtar Kavram

Converting units between the US Customary and metric systems using a given conversion factor, followed by basic arithmetic subtraction.

Soru 457Soru →

When the expression $\frac{(8.0 \times 10^4) \times (6.0 \times 10^{-7})}{1.5 \times 10^3}$ is evaluated and the result is written in standard scientific notation as $a \times 10^n$ , where $1 \le a < 10$ , what is the value of the integer $n$ ?

Cevabı ve açıklamayı göster

Cevap: -5

Cevap

The exponent is -5.

Evaluating the numerator yields

48 \times 10^{-3}

. Dividing this by the denominator

1.5 \times 10^3

results in

32 \times 10^{-6}

. To write this in standard scientific notation, the coefficient must be strictly greater than or equal to 1 and strictly less than 10, so 32 is rewritten as

3.2 \times 10^1

. Applying this shift makes the final expression

3.2 \times 10^{-5}

. Thus, the final exponent

n

is -5.

Adım Adım Çözüm

1

Multiply the expressions in the numerator

48 \times 10^{-3}

Following the order of operations, simplify the numerator first by multiplying the coefficients (

8.0 \times 6.0 = 48

) and adding the exponents of the base 10 (

4 + (-7) = -3

).

2

Divide by the denominator

32 \times 10^{-6}

Divide the resulting numerator's coefficient by the denominator's coefficient (

48 \div 1.5 = 32

) and subtract the denominator's exponent from the numerator's exponent (

-3 - 3 = -6

).

3

Normalize the coefficient to standard scientific notation

3.2 \times 10^{-5}

Standard scientific notation requires the coefficient (

a

) to be between 1 and 10. We rewrite

32

as

3.2 \times 10^1

. Multiplying this by the existing

10^{-6}

changes the overall exponent to

1 + (-6) = -5

.

4

Identify the final value of

n

-5

The question asks for the integer

n

from the format

a \times 10^n

. Comparing our final result

3.2 \times 10^{-5}

to this format,

n = -5

.

Anahtar Kavram

Operations with scientific notation and coefficient normalization

Soru 458Soru →

What is the smallest positive integer that is a multiple of both $8$ and $12$ ?

Cevabı ve açıklamayı göster

Cevap: 24

Cevap

24

The smallest positive integer that is a multiple of both

8

and

12

is their least common multiple (LCM). The multiples of

8

are

8, 16, 24, 32, \dots

and the multiples of

12

are

12, 24, 36, \dots

. The smallest number that appears in both lists is

24

.

Adım Adım Çözüm

1

Find the positive multiples of

8

.

8, 16, 24, 32, 40, \dots

We need to determine a number that is a multiple of

8

.

2

Find the positive multiples of

12

.

12, 24, 36, 48, \dots

We need the number to also be a multiple of

12

.

3

Identify the smallest common multiple from both lists.

24

The question asks for the smallest positive integer that is a multiple of both numbers.

Anahtar Kavram

Least Common Multiple (LCM)

Tahmini Süre:45s

Soru 459Soru →

In a medical supply drop, the ratio of bandages to antiseptic bottles is $7:3$ . If there are $210$ antiseptic bottles in the drop, how many bandages are included?

Cevabı ve açıklamayı göster

Cevap: 490

Cevap

490

The proportion must match the quantity of bandages to antiseptics. Since the ratio is

7

parts bandages for every

3

parts antiseptics, and the actual number of antiseptics is

210

(

70

times the ratio amount), the number of bandages must also be

70

times its ratio amount. Therefore,

7 \times 70 = 490

bandages.

Adım Adım Çözüm

1

Identify the known ratio and the known quantity.

The ratio of bandages to antiseptics is

7:3

, and there are

210

antiseptics.

To correctly set up a mathematically accurate proportion.

2

Set up the proportion equation.

\frac{7}{3} = \frac{x}{210}

To relate the given simplified ratio to the actual numbers.

3

Solve the proportion for

x

.

x = \frac{7 \times 210}{3} = 7 \times 70 = 490

To find the unknown number of bandages.

Anahtar Kavram

Solving basic proportions from a given part-to-part ratio

Tahmini Süre:45s

Soru 460Soru →

During a field exercise, a combat engineer platoon's daily fuel consumption increased by $20\%$ in the first week, and then decreased by $25\%$ in the second week. If the final fuel consumption was $4,500$ gallons per day, what was the initial daily fuel consumption in gallons?

Cevabı ve açıklamayı göster

Cevap: 5000

Cevap

5000

The correct calculation requires treating the percentage changes as sequential multipliers. The initial amount increases by

20\%

(multiplier of

1.20

) and the new amount decreases by

25\%

(multiplier of

0.75

). The combined net multiplier is

1.20 \times 0.75 = 0.90

, meaning the final value is

90\%

of the initial value. To find the initial value, we divide the final amount (

4,500

) by

0.90

, which yields

5,000

.

Adım Adım Çözüm

1

Determine the multipliers for the successive percentage changes.

A

20\%

increase is represented by

1.20

, and a

25\%

decrease is represented by

0.75

.

Successive percentage changes must be multiplied consecutively, not added together.

2

Set up an equation representing the net change.

x \times 1.20 \times 0.75 = 4500

The initial amount (

x

) multiplied by each successive change equals the final amount.

3

Calculate the combined multiplier.

1.20 \times 0.75 = 0.90

Simplifying the multipliers shows that the net change is a

10\%

decrease overall.

4

Solve the equation for the initial amount.

x = \frac{4500}{0.90} = 5000

Dividing the final consumption by the combined multiplier isolates

x

to find the original amount.

Anahtar Kavram

Successive Percentage Changes and Reverse Percentages

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram