100 cans and 300 bottles were bought for $450. 200 cans and 200 bottles were bought for $400. What is the cost of an individual can and bottle?

Answer 1

100c + 300b = 450

200c + 200b = 400

-2(100c + 300b = 450)

-400b = -500

b = 1.25 or

c = .75 (by substitution)

Answer 2

100x + 300y = 450

200x + 200y = 400

You can you elimination here but multiplying the top equation by -2

-200x + -600y = -900

200x + 200y = 400

Subtract down

-400y = -500

divide by -400

y = 1.25

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Plug Y back into the original equation to find x

100x + 300(1.25) = 450

100x + 375 = 450

subtract 375 from both sides

100x = 75

divide by 100

x = .75