Amy bought 16 forks and 12 spoons for $106.40. Ben bought 10 forks and 6 spoons for $60.20. Cathy wants to buy 5 forks and 5 spoons. How much would Cathy have to pay?

Question

(i need to solve by a non-algebraic solution)

Answer 1

i couldn't really think of a solution which is non-algebraic. but i just tried to simplify things in this solution:

16 Forks + 12 Spoons = 106.40
therefore, if we get the half of both the number of forks and spoons, the price will also be half:
8 Forks + 6 Spoons = 53.20
the other given is
10 Forks + 6 Spoons = 60.20
thus we'll be able to get the price of 2 Forks if we subtract both:
10 Forks + 6 Spoons = 60.20
8 Forks + 6 Spoons = 53.20
--------------------------------
2 Forks = 7.00
thus the price of one fork is,
1 Fork = 3.50
bow we substitute this to either condition (in this case, to 2nd condition):
10*3.50 + 6 Spoons = 60.20
6 Spoons = 60.20 - 35.00
6 Spoons = 25.20
1 Spoon = 4.20
therefore the price of 5 Forks and 5 Spoons is:
5*3.50 + 5*4.20 = $ 38.50

hope this helps~ :)

Answer 2

yes, thanks a billion!