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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?

User Donk
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1 Answer

2 votes

Answer:

The length of 1 pencil is 2.8 inches and the length of 1 crayon is 1.4 inches

Explanation:

Let the length of one pencil be p.

Let the length of one crayon be c.

5 pencils and 4 crayons are 19.6 inches. Therefore:

5p + 4c = 19.6 ___________ (1)

6 pencils and 5 crayons are 23.8 inches. Therefore:

6p + 5c = 23.8 ___________ (2)

We now have two simultaneous equations:

5p + 4c = 19.6 ___________ (1)

6p + 5c = 23.8 ___________(2)

Multiply (1) by 6 and (2) by 5, we have:

30p + 24c = 117.6 _________(3)

30p + 25c = 119 __________ (4)

Subtract (3) from (4), we have:

30p + 25c - (30p + 24c) = 119 - 117.6

30p - 30p + 25c - 24c = 1.4

=> c = 1.4 inches

Put the value of c in (1), we have:

5p + 4(1.4) = 19.6

5p + 5.6 = 19.6

=> 5p = 19.6 - 5.6

5p = 14

p = 14 / 5

p = 2.8 inches

The length of 1 pencil is 2.8 inches and the length of 1 crayon is 1.4 inches.

User Jiang Bian
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