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?

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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:

1. and


2. 

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.