SOLUTION: 6 pencils and 5 crayons are 25.7 inches. 7 pencils and 6 crayons are 30.2 inches. Each pencil is the same length as the other pencils, and each crayon is the same length as the oth

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Question 1194256: 6 pencils and 5 crayons are 25.7 inches. 7 pencils and 6 crayons are 30.2 inches. Each pencil is the same length as the other pencils, and each crayon is the same length as the other crayons. What is the length of 1 pencil? What is the length of 1 crayon?

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39621) (Show Source):
You can put this solution on YOUR website!
simple system of equations in two variables application

Maybe a little easier try to eliminate c and find p.

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Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

The information in this problem makes it easier to solve using a non-standard algebraic method.

(1) 7p+6c = 30.2
(2) 6p+5c = 25.7

Subtract the (2) from (1):

(3) p+c = 4.5

Multiply that by 5:

(4) 5p+5c = 22.5

Subtract (4) from (2):

(5) p = 25.7-22.5 = 3.2

Subtract (5) from (3):

(6) c = 1.3

ANSWERS:
pencil: 3.2 inches
crayon: 1.3 inches

Note that formal algebraic solution corresponds to the following solution using common sense:

7 pencils and 6 crayons have a total length of 30.2 inches
6 pencils and 5 crayons have a total length of 25.7 inches
therefore, 1 pencil and 1 crayon have a total length of 30.2-25.7 = 4.5 inches
therefore, 5 pencils and 5 crayons have a total length of 5*4.5 = 22.5 inches
therefore, 1 pencil has a length of 25.7-22.5 = 3.2 inches
therefore, 1 crayon has a length of 4.5-3.2 = 1.3 inches