Question

1. write an expression for each of the verbal descriptions below.

statement expression
a. the perimeter of a rectangle with length of 3 times a number and width of 2 times a different number.
b. the square of the difference between p and q.
c. six less than the quotient of m and n.
d. the sum of three times a number and twice another number.

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter of a rectangle is $P = 2(l + w)$. Let the first number be $x$ and the second number be $y$. The length $l = 3x$ and the width $w=2y$. So the perimeter expression is $2(3x + 2y)=6x + 4y$.

Step2: Translate "square of the difference"

The difference between $p$ and $q$ is $p - q$. The square of this difference is $(p - q)^2$.

Step3: Translate "quotient and less - than"

The quotient of $m$ and $n$ is $\frac{m}{n}$. Six less than this quotient is $\frac{m}{n}-6$.

Step4: Translate "sum of multiples of numbers"

Let the first number be $a$ and the second number be $b$. Three times the first number is $3a$ and twice the second number is $2b$. The sum is $3a + 2b$.

Answer:

A. $6x + 4y$
B. $(p - q)^2$
C. $\frac{m}{n}-6$
D. $3a + 2b$