Answer:
24 and 41 inches.
Step-by-step 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:
[tex]a+b=65[/tex]
One piece, say b, is 7 inches shorter than twice the length of the other, a.
Therefore, we can write the following equation:
[tex]b=2a-7[/tex]
The “2a” represents the twice, and the “-7” represents the 7 shorter inches.
We now have a system of equations:
[tex]\left\{\begin{array} \ a+b=65\\ b=2a-7\end{array}[/tex]
We can solve using substitution. Substitute the second equation into the first. Hence:
[tex]a+(2a-7)=65[/tex]
Combine like terms:
[tex]3a-7=65[/tex]
Add 7 to both sides:
[tex]3a=72[/tex]
Divide both sides by 3:
[tex]a=24[/tex]
So, the shorter piece is 24 inches.
Then, we can use our second equation again:
[tex]b=2a-7[/tex]
Since we now know a, substitute 24 for a and evaluate. Hence:
[tex]\begin{aligned} b&=2(24)-7\\&=48-7\\&=41\end{aligned}[/tex]
Therefore, the length of the other two pieces are 24 and 41 inches.
