Problema Solution
I subscribe to the Comic-of-the-Month Club. Each month I can buy any number of the 48 titles offered by the club. The first month I bought five comics for $3.07. The second month I bought two comics for $1.72. The next month I bought six of the club offerings for $3.52. In May I bought three more for a charge of $2.17. The club charges a handling fee and then a fee for each comic. How much would it have cost to buy all 48 titles at the same time?
Answer provided by our tutors
The club charges a handling fee and then a fee for each comic.
let
h = the handling fee
c = the fee for each comic
First month: 5 comics for $3.07
5c + h = 3.07
Second month: 2 comics for $1.72
2c + h = 1.72
Third month: 6 comics for $3.52
6c + h = 3.52
May: 3 comics for $2.17
3c + h = 2.17
using the equations from the second month and May we form the system of equations
2c + h = 1.72
3c + h = 2.17
by solving it we find
h = $0.82
c = $0.45
click here to see the step by step solution of the system of equations
Indeed
First month: 5 comics for $3.07
5*0.45 + 0.82 = 3.07
Second month: 2 comics for $1.72
2*0.45 + 0.82 = 1.72
Third month: 6 comics for $3.52
6*0.45 + 0.82 = 3.52
May: 3 comics for $2.17
3*0.45 + 0.82 = 2.17
to by all 48 tittles at the same time would cost: to cost for 48 comics + handling fee
48*0.45 + 0.82 = $22.42
to buy all 48 titles at the same time would cost $22.42.