Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 6

10 / 11

A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

Answer

1
Let the length of the shorter piece be x feet. Express the length of the longer piece using the given relationship.
Shorter piece = $x$ feet
Longer piece = $4x$ feet
2
Use the total length of the fence to find x.
\text{$x + 4x = 300$ $\quad$ ${color:#625b5f}[Total length of fence = 300 feet]{/color}$}
⇒
$5x = 300$
⇒
\text{ $x = \dfrac{300}{5}$}
⇒
\text{ $x = 60$ feet $\quad$ ${color:#625b5f}[Length of the shorter piece]{/color}$}
3
Find the length of the longer piece.
\text{$4x = 4 × {color:#2E2EFF}60{/color} = 240$ feet $\quad$ ${color:#625b5f}[Length of the longer piece]{/color}$}
4
Write the lengths of the two pieces.
Answer: The shorter piece is 60 feet long and the longer piece is 240 feet long.
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