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A merchant sells three different sizes of canned tomatoes. A large can costs as much as 5 medium cans, or 7 small cans. If a customer buys an equl number of small and large cans of tomatoes for the exact amount of money that would buy 200 medium cans, how many small cans will she buy? HELP! HOW DO I SET THIS EQUATION UP?

Respuesta :

Hi there,

The answer is she can buy 28 small cans. She can also buy 40 medium cans with the same. I gonna explain how I did that way you know if you be ask for explanation here we go. I did 200 divided by 5 = 40 small cans and you also do the same  by the medium 200 divided by 5 = 40 small cans. you can also add and add that will take long time.

I hope I did easy way to make you understand.
let L = cost of 1 large, M = cost 1 medium and S = cost of 1 small can
now we can write some equations relating these variables:
L = 5M =>M = L/5
L = 7S => S = L/7
200M = xL + xS where x = number of small and large cans

[tex]200 \frac{L}{5} =xL+x \frac{L}{7} \\ \\40L=Lx+ \frac{L}{7} x \\ \\280L=7Lx+Lx \\ \\280L=8Lx \\ \\x= \frac{280L}{8L} =35[/tex]

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