Question 542645: A board is 118cm long. Karen cut it into two pieces, with one piece 4cm longer than the other. Find the length of both pieces.
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! The 118 cm long board was divided into two pieces of unequal length. We will call the length of the longer of these pieces 'L' and the length of the shorter piece 'S'.
Because the length of the two pieces of the board add up to 118, we can state the equation, 'L+S=118.'
Because we know the longer piece is 4 inches greater than the shorter piece, we can state the equation 'L=S+4'
We can substitute the value for 'L', which we got from the second equation, into the first equation.
L=S+4
L+S=118
S+4+S=118
First, we can combine the two 'S' terms into '2S'.
2S+4=118
Next, we subtract 4 from both sides of the equation.
2S+4-4=118-4
2S=114
Then, we divide both sides of the equation by 2.
2S/2=114/2
S=57
Finally, we can substitute this value of S into the equation 'L=S+4' to find the value of the longer piece.
L=S+4
L=57+4
L=61
So, the lengths of the boards are 57 cm and 61 cm.
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