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While doing back to school shopping on tax-free weekend, Mrs. Michaels bought 2 packs of mechanical pencils and 3 binders for a total cost of $21.00. Mr. Lawrence bought 5 of the same packs of mechanical pencils and 2 of the same binders for a total of $25.00. How much does each pack of pencils cost? *

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Answer:

$3.00  

Step-by-step explanation:

Let p = the cost of a pack of pencils

and b = the cost of a binder

Then we have two simultaneous equations.

(1)  2p + 3b  = 21.00

(2) 5p + 2b = 25.00

1. Multiply each equation by numbers to give one of the variables the same coefficient.

Multiply (1) by 2 and (2) by 3.This gives

(3)  4p + 6b = 42.00

(4) 15p + 6b = 75.00

2. Subtract (3) from (4)

This gives

(5) 11p = 33.00

3. Solve equation (5) for p

Divide each side by 11

p = 3.00

Each pack of pencils costs $3.00.

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