Question

The cafeteria sells each apple at one price and each banana at another price. For 5 apples and 3 bananas Dan pays $5.70. For 3 apples and 5 bananas Chris pays $4.70. The price of one apple is how much more then the price of one banana, in cents?

Answer 1

50

Explanation:

a = # of apples

b = # of bananas

5a + 3b = 570

3a + 5b = 470

Solve with substitution or elimination. To solve by elimination, multiply the first equation by 5 and the second equation by 3.

25a + 15b = 2850

9a + 15b = 1410

Subtract:

16a = 1440

a = 90

Plug into either equation to find b.

5(90) + 3b = 570

450 + 3b = 570

3b = 120

b = 40

So apples are 90 cents, and bananas are 40 cents. Therefore, apples are 50 cents more than bananas.