how should they spend their money

Question

643.Pat has $48 and Kim has $24, so the ratio of Pat’s money to Kim’s money is 2:1. If they both spend $5, is the ratio still 2:1? Explain how they could spend their money so that the ratio of Pat’s money to Kim’s money remains 2 : 1.

Answer 1

First, notice that the ratio 2:1 is obtained because

(Pat's Money)/(Kim's Money) = 48/24 =2/1 or 2:1.

Now, suppose they each spent $5. Then, Pat now has $48-$5 = $43 and Kim now has $24-5 = $19. We can see now that

(Pat's Money)/(Kim's Money) = 43/19,

which is not equal to 2/1 so the ratio does not remain the same.

To determine how to keep their ratio the same, suppose Pat spends $x and Kim spends $y. Then we want to solve for x in terms of y (or y in terms of x) in the following equation:

(48 - x)/(24 - y) = 2/1 = 2

Multiplying by 24-y in both sides,

48 - x = 48 - 2y

Simplifying, we see x = 2y. This tells us that Pat must spend two times as much money as Kim in order to keep the same ratio.