Question

6 pencils and 5 crayons are 37.5 inches. 7 pencils and 6 crayons are 44.1 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 1

Answer: The length of a pencil is 4.5 inches. The length of a crayon is 2.1 inches.

Explanation:

Let pencils be p

Let crayons be c

6 pencils and 5 crayons are 37.5 inches. This will be:

6p + 5c = 37.5 ........ equation i

7 pencils and 6 crayons are 44.1 inches. This will be:

7p + 6c = 44.1 ........ equation ii

Combine both equations together

6p + 5c = 37.5 ......... i

7p + 6c = 44.1 .......... ii

Multiply equation i by 7

Multiply equation ii by 6

42p + 35c = 262.5 ....... iii

42p + 36c = 264.6 ........ iv

Subtract iv from iii

c = 2.1

Plug the value of c into equation i

From equation i

6p + 5c = 37.5

6p + 5(2.1) = 37.5

6p + 10.5 = 37.5

6p = 37.5- 10.5

6p = 27

p = 27/6

p = 4.5

The length of a pencil is 4.5 inches. The length of a crayon is 2.1 inches.