SOLUTION: 5 pencils and 4 crayons are 19.6 inches. 6 pencils and 5 crayons are 23.8 inches. Each pencil is the same length as the other pencils, and each crayon is the same length as the oth

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 5 pencils and 4 crayons are 19.6 inches. 6 pencils and 5 crayons are 23.8 inches. Each pencil is the same length as the other pencils, and each crayon is the same length as the oth      Log On

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Question 1158795: 5 pencils and 4 crayons are 19.6 inches. 6 pencils and 5 crayons are 23.8 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?
Answer by greenestamps(13203) About Me  (Show Source):
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The difference between the two measurements is 1 more pencil and 1 more crayon for 4.2 more inches.

So the length of 4 pencils and 4 crayons is 4(4.2) = 16.8 inches.

Then comparing that to 5 pencils and 4 crayons with a total lengths of 19.6 inches, we find the length of 1 pencil is 19.6-16.8 = 2.8 inches.

And then the length of one crayon is 4.2-2.8 = 1.4 inches.

That common sense solution is equivalent to one of many possible solutions using formal algebra:
(1)  5p+4c = 19.6    (given)
(2)  6p+5c = 23.8    (given)
(3)  p+c = 4.2       (2)-(1)
(4)  4p+4c = 16.8    4*(3)
(5)  p = 2.8         (1)-(4)
(6)  c = 1.4         (3)-(5)