SOLUTION: one board is three feet shorter than twice the length of the other board. if the two boards together are 15 ft long, how long is each board?

Question 3395: one board is three feet shorter than twice the length of the other board. if the two boards together are 15 ft long, how long is each board?
Answer by drglass(89) (Show Source): You can put this solution on YOUR website!
Start by naming the boards, we can call the first board x and the second board y. The problem tells us that x is three feet shorter than twice the length of y. Well, twice the length of y is and three feet less than 2y is , therefore "x is three feet shorted than twice the length of y" can be written . The other part of the problem tells us that together the boards are 15 ft, which means

So what do we have:

Now, let's subtract y from both sides of the second equation. This gives us:

Substitute this equation for x into x in the first equation

.
add y to both sides to get ,
add 3 to both sides to get ,
now divide both sides by 3 to get .
Substitue y = 6 into the first equation and we get:

.
So one board is 6 ft and the other is 9 ft.
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