algebra word problem

Question

Five pencils and three erasers cost 65 cents. Three pencils and two erasers cost 40 cents. Find the cost of one pencil and the cost of one eraser.

Answer 1

let p and e variables stand for pencils and erasers respectively.

Here's what we know:

5p + 3e = 65

3p + 2e = 40

 

It's not an easy elimination style, but we can probably use elimination if we multiply the two equations by 2 and -3 respectively:

10p + 6e = 130

-9p - 6e = 120

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p = 10 cents

 

Now that we know p, we can solve for e and check:

5 * 10 + 3e = 65

50 + 3e = 65

3e = 15

e = 5 cents

 

3 * 10 + 2 * 5 = 40

30 + 10 = 40

40 = 40