SOLUTION: Help!! I cant translate sentences into equations very well. Im still new to algebra. A board 18ft long is cut into two pieces. Two feet less than the product of five and the length

Question 10976: Help!! I cant translate sentences into equations very well. Im still new to algebra. A board 18ft long is cut into two pieces. Two feet less than the product of five and the length of the smaller piece is equal to the difference between three times the length of the longer piece and eight. Find the length of each piece. If I can see how to set up this problem, I know I can solve it. Please help! Thanks
Found 2 solutions by Earlsdon, rapaljer:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
This is one of the skills you would do well to develop...translating English to Algebra.
Let the length of the longer piece be L and the length of the shorter piece be (18-L) Let's set up an equation from the problem description:
Two feet less than (subtract 2 ft. from) the product of 5 and the length of the smaller piece (5(18-L)) is equal to (=) the difference (subtract) between three times the length of the longer piece (3L) and eight (8) or (3L - 8). Putting it all together, we get:
Simplify and solve for L
Go ahead and try this.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let x = length of the smaller piece

Since the total length is 18 feet, the rest of the board is 18-x.
18-x = longer piece.

The equation comes from the second sentence:
"Two feet less than the product of five and the length of the smaller piece is equal to the difference between three times the length of the longer piece and eight."

5( smaller piece) less 2 feet is 3(longer piece) - 8
5(x) - 2 = 3(18-x) - 8
5x - 2 = 54 - 3x - 8
5x - 2 = 46 - 3x

Add 3x to each side to get all the x terms on the left side:
5x + 3x - 2 = 46 - 3x + 3x
8x - 2 = 46

Add +2 to each side of the equation:
8x - 2 + 2 = 46 + 2
8x = 48
x=6 feet. Smaller piece
18-x = 12 feet. Larger piece.

Check: 2 less than five times the smaller piece = 30-2 = 28 feet
Three times longer - 8 = 36 - 8 = 28 feet.
It checks.

R^2 at SCC

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