A board 60 in. long is cut into two parts so that the longer piece is 5 times the shorter. What are the lengths of the two pieces?

Question

The shorter piece is ___  in.

The longer piece is ____  in.

Answer 1

let p₁ and p₂ be the two board pieces.

The length of one board is 5x the length of the other board so

p₁ = 5p₂

The sum of the two pieces is 60 inches

p₁ + p₂ = 60

Substitute p₁ = 5p₂

5p₂ + p₂ = 60

6p₂ = 60

p₂ = 10

Put that into the 2nd equation

p₁ + 10 = 60

p₁ = 50

So the shorter piece is 10 inches and the longer piece is 50 inches.

Answer 2

L=5S

L+S = 60

5S+S = 60

6S = 60

S = 60/6 = 10 inches

L=5S = 5(10) = 50 inches

50+10=60