Problem Solving

BTGmoderatorDC wrote:The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months. Which of the following represents food purchases, in dollars, for the first 9 months of a year?

A)9y - xy/100

B)9y + xy

C)9y - xy

D)(9y-xy)/9

E)y-xy/6

This is a Variables in the Answer Choices question (VIAC). This question type can be answered algebraically or using the INPUT-OUTPUT approach.
Mitch has demonstrated the INPUT-OUTPUT approach, so let's solve the question algebraically.

The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months.
In other words, January's food purchase amount is x percent less than y
x percent = x/100
So, x percent of y = (x/100)(y) = xy/100
So, January's food purchase amount = y - xy/100

Which of the following represents food purchases, in dollars, for the first 9 months of a year?
January's food purchase amount = y - xy/100
The food purchase amount for EACH of the other 8 months = y

So, the TOTAL cost = y - xy/100 + y + y + y + y + y + y + y + y
= y - xy/100 + 8y
= 9y - xy/100

Answer: A

Cheers,
Brent

BTGmoderatorDC wrote:The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months. Which of the following represents food purchases, in dollars, for the first 9 months of a year?


A)9y - xy/100

B)9y + xy

C)9y - xy

D)(9y-xy)/9

E)y-xy/6

OA A

Source: Princeton Review

For 8 months, not counting January, the total expenditure for food is 8y.

In January, the amount spent on food is (100 - x)/100 * y = (100y - xy)/100

So for the first 9 months, the total expenditure for food is:

8y + (100y - xy)/100

Getting a common denominator,we have:

800y/100 + (100y - xy)/100

(900y - xy)/100 = 900y/100 - xy/100 = 9y - xy/100

Answer: A