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27 votes
A 24 foot board is cut into two pieces so that the smaller piece measures x feet. If the longer piece is 6 feet less than twice the shorter piece, what is the length of both sides?

User Lbarbosa
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1 Answer

9 votes
9 votes

Answer:

The smaller piece is 10 feet long, and the longer one is 14 feet long

Explanation:

We can use variables.

A 24 foot board is cut into 2 pieces, the longer one, l, is 6 feet shorter than twice the shorter one, so the equation we can turn this into is: 2m - 6 + m = 24. the 2m - 6 is the longer piece, since it is 6 feet less (-6) than twice the shorter piece (2m). The other "m" is the smaller piece. so we have:

2m - 6 + m = 24

Add 6 to both sides:

2m + m = 30

Simplify:

3m = 30

Divide both sides by 3:

m = 10. So the shorter piece is 10 feet.

If the shorter piece is 10 feet, then the longer one is 24 - 10 = 14 feet

Now we check our answer:

The longer piece is 6 less than twice the shorter piece, so if we add 6 to the longer piece, and then divide it by 2, it should equal the shorter piece's length:

14 + 6 = 20, 20/2 = 10. this is the length of the shorter piece, so it is true

The smaller piece is 10 feet long, and the longer one is 14 feet long

User Wfoster
by
2.9k points
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