Question

You spend $24 on 21 pounds of apples. You purchase 2 pounds of golden apples for $1.25 per pound. Red delicious apples cost $1.00 per pound and empire apples cost $1.50 per pound. How many pounds of each type of apple did you purchase?

Answer 1

2 pounds of Golden Apples

5 pounds of Empire Apples

14 pounds of Red Apples

Explanation:

2 pounds of golden apple for 1.25 per pound = 2 * 1.25 = $2.50 spent

24 - 2.5 = $21.5 left for red apples and empire apples

Also, 2 pounds of 21 pounds gone, so 19 pounds left

Now,

let number of red apples be r and number of empire apples be e

So, we can write:

r + e = 19 [also r = 19 - e]

and

1r + 1.5e = 21.5

Putting #1 in #2 equation, we solve for e:

`1r + 1.5e = 21.5\\1(19-e)+1.5e=21.5\\19-e+1.5e=21.5\\0.5e=2.5\\e=5`

Thus, r = 19 - e, 19 - 5 = 14

So,

2 pounds of Golden Apples

5 pounds of Empire Apples

14 pounds of Red Apples