Answer & Explanation
A 20 foot board is cut into two pieces whose lengths are in the ration of 7 to 3. Find the length of the longer piece.
7 to 3 is the same as 7x to 3x where 7x is the longer piece.
Let x denote the length of one piece of the board in feet.
Since the two pieces of the board are in the ratio of 7 to 3, it follows that the other piece has a length of
Given the total length equal to 20 feet, an equation can be set-up as shown below.
Multiply by 3 on both sides of the equation.
Divide throughout by 10 to get,
If x=6, then we have
Therefore, the lengths of the two pieces are 6 feet and 14 feet.
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