Question

A machine cuts a strip of carpet into two pieces. The length of the smaller piece is 5 meters greater than  the length of the larger piece. If the length of the smaller piece is 12 meters, the length of the bigger piece is meters and the total length of the carpet is meters.

Answer 1

`\bf \stackrel{\stackrel{small~piece}{length}}{a}=\stackrel{\stackrel{large~piece}{length}}{b}+5\impliedby \begin{array}{llll} \textit{small piece's length}\\ \textit{ 5 longer than large piece's length} \end{array} \\\\\\ a=12\qquad \qquad 12=b+5\implies 12-5=b\implies 7=b`

so, the total length of the carpet is just a+b.

Answer 2

The length of the bigger piece is 17 meters

and the total length of the carpet is 29 meters.

Explanation:

The length of the smaller piece is 5 meters greater than the length of the larger piece.

i.e. Length of larger piece=Length of smaller piece+5

The length of the smaller piece is 12 meters.

So, Length of larger piece=12+5

=17 meters

Total Length of carpet=Length of smaller piece + Length of larger piece

= 12+17

= 29 meters

Hence, the length of the bigger piece is 17 meters

and the total length of the carpet is 29 meters.