Question

You buy 1 box of dog food and 2 cans of cat food for $23. Your friend buys 2 boxes of dog food and 1 can of cat food for $22. What is the cost of each box of dog food? of each can of cat food?

Each box of dog food costs $
and each can of cat food costs $

Answer 1

• dog food: $7
• cat food: $8

Explanation:

You want the price of a box of dog food and a can of cat food if these purchases were made:

• 1 boxes + 2 cans for $23
• 2 box + 1 can for $22

Setup

The equations describing these purchases can be written as ...

b + 2c = 23

2b +c = 22

Solution

Substituting for c, we have ...

c = 22 -2b

b +2(22 -2b) = 23

-3b +44 = 23 . . . . . . . simplify

21 = 3b . . . . . . . . . add 3b -23

7 = b . . . . . . . . . divide by 3

c = 22 -2(7) = 8

Each box of dog food costs $7; each can of cat food costs $8.

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