Distance/Revenue

Question

A woman bought a number of items for $60. She realized that if she had bought 6 more items for the same money, she would have paid $5 less per item. How many items did she buy?

Answer 1

Let N = the number of items bought, and P = the price for each.

The total cost was N * P = 60

The 2nd sentence tells us that (N + 6) * (P - 5) = 60

From the 1st equation, P = 60/N. Use this to replace P in the 2nd equation:

(N + 6) * (60/N - 5) = 60

Multiply it out and simplify:

60 + 360/N - 5N - 30 = 60

360/N - 5N = 30

360 - 5N^2 = 30N

5N^2 + 30N - 360 = 0

N^2 + 6N - 72 = 0

Factor this to get the roots---you'll only use the positive one:

N = +6

CHECK: P = 10

N + 6 = 12

P - 5 = 5

The product is still 60

Answer 2

x=$60

x+6=$60-$5x

54=6x

x=9