SOLUTION: I can't find what category this would be but the section says Problem solving Consecutive Integers. The problem says The lenghters in feet of three ropes are consecutive multiples

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Question 121331: I can't find what category this would be but the section says Problem solving Consecutive Integers. The problem says The lenghters in feet of three ropes are consecutive multiples of 3. If each rope were 4ft shorter, the sum of their lengths would be 42ft. Could you walk me thourgh how to do this.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the first rope be 3x feet.
The 3x insures that the length is a multiple of 3 feet.
The next rope will then measure (3x+3) feet. This the next consecutive multiple of 3.
And the third rope will measure (3x+6) feet.
Now if we reduce each of the three lengths by 4 feet then add them together, their sum is to equal 42 feet.
Now we can write an equation to solve this:
%283x-4%29%2B%283x%2B3-4%29%2B%283x%2B6-4%29+=+42 Combine like-terms.
9x-12%2B9+=+42
9x-3+=+42 Add 3 to both sides.
9x+=+45 Divide both sides by 9.
x+=+5
The length of the first rope is 3x = 3(5) = 15 feet.
The length of the second rope is 3x+3 = 3(5)+3 =18 feet.
The length of the third rope is 3x+6 = 3(5)+6 = 21 feet.
Check:
Add the lengths (minus 4 ft.) of the three ropes.
%2815-4%29%2B%2818-4%29%2B%2821-4%29+=+11%2B14%2B17 = 42