Which of the following algebraic expressions correctly represents the statement: 'Five les… — Armed Services Vocational Aptitude Battery (ASVAB)

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'?

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

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

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.

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.

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.

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