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?

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

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~ :)

yes, thanks a billion!

To solve this problem without using algebra, we can first determine the cost per fork and the cost per spoon.

Amy bought 16 forks and 12 spoons for $106.40, so the cost of each fork can be calculated by dividing the total cost by the number of forks: 106.40 / 16 = $6.65 per fork. Similarly, the cost of each spoon can be calculated by dividing the total cost by the number of spoons: 106.40 / 12 = $8.87 per spoon.

Ben bought 10 forks and 6 spoons for $60.20. Using the same approach, we can calculate the cost of each fork: 60.20 / 10 = $6.02 per fork. For the spoons: 60.20 / 6 = $10.03 per spoon.

Now that we know the cost per fork and cost per spoon for both Amy and Ben, we can calculate the total cost for Cathy's purchase.
Cathy wants to buy 5 forks and 5 spoons.

For the forks, using Amy's price per fork of $6.65, the total cost would be: 5 forks * $6.65 = $33.25.
For the spoons, using Ben's price per spoon of $10.03, the total cost would be: 5 spoons * $10.03 = $50.15.

Therefore, Cathy would have to pay $33.25 + $50.15 = $83.40.