PSAT Math Grid-Ins Question 133: Answer and Explanation

Question: 133

At a particular store, customers can purchase children's outfits for $20 and adults' outfits for $45. If a family purchased 22 outfits for a total of $765, how many children's outfits did the family purchase?

Correct Answer: 9

Explanation:

(9) Let's call c the number of children's outfits purchased and a the number of adults' outfits purchased. We can write two equations: one for the number of outfits purchased and one for the amount of money spent.

We know that the sum of children's outfits and adults' outfits purchased must add up to $22:

c + a = 22

We also know that each children's outfit was $20, so the amount of money spent on children's outfits was 20c. Similarly, each adults' outfit was $45. So the amount of money spent on adults' outfits was 45a. We are also told that the family spent a total of $765. Therefore, our second equation is:

20c + 45a = 765

We want to know how many children's outfits were purchased. Let's solve for a in the first equation so that we can substitute a out of the second equation, leaving only c-terms.

a = 22 - c

Plug this into the second equation:

20c + 45(22 - c) = 765

Distributing the 45 gives us:

20c + 990 - 45c = 765

We can now combine both c-terms on the left:

-25c + 990 = 765

Subtracting 990 from both sides leaves:

-25c = -225

Finally, dividing both sides by -25 will tell us the number of children's outfits purchased:

c = 9