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.

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:

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

Therefore, we can write the following equation:

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

We now have a system of equations:

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

Combine like terms:

Add 7 to both sides:

Divide both sides by 3:

So, the shorter piece is 24 inches.

Then, we can use our second equation again:

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

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

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step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse