Question

A board 65 inches long is sawed into two pieces, so that one piece is 7 inches shorter than twice the length of the other piece. Find the length of the two pieces.

Answer 1

50.3333333+14.6666667 =65

Explanation:

Answer 2

24 and 41 inches.

Explanation:

Let the lengths of the two pieces be a and b.

The total length of the two piece should be the length of the original board. Therefore:

`a+b=65`

One piece, say b, is 7 inches shorter than twice the length of the other, a.

Therefore, we can write the following equation:

`b=2a-7`

The “2a” represents the twice, and the “-7” represents the 7 shorter inches.

We now have a system of equations:

`\left\{\begin{array} \ a+b=65\\ b=2a-7\end{array}`

We can solve using substitution. Substitute the second equation into the first. Hence:

`a+(2a-7)=65`

Combine like terms:

`3a-7=65`

Add 7 to both sides:

`3a=72`

Divide both sides by 3:

`a=24`

So, the shorter piece is 24 inches.

Then, we can use our second equation again:

`b=2a-7`

Since we now know a, substitute 24 for a and evaluate. Hence:

`\begin{aligned} b&=2(24)-7\\&=48-7\\&=41\end{aligned}`

Therefore, the length of the other two pieces are 24 and 41 inches.