Answer:
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:
a + b = 65
b = 2a - 7
We can solve using substitution. Substitute the second equation with 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:
b = 2(24) - 7
= 48 - 7
= 41
Therefore, the length of the other two pieces is 24 and 41 inches.