The lengths in feet of three ropes are consecutive multiples of three. If each rope were four feet shorter, the sum of their lengths would be 42 feet. Find the lengths of the three ropes.
To solve this problem, let's start by setting up some equations.
Let's say the lengths of the three ropes are x feet, (x + 3) feet, and (x + 6) feet. Since the lengths are consecutive multiples of three, we can express them as x, 3x, and 6x.
Now, if we were to subtract 4 feet from each rope length, the new lengths would be (x - 4) feet, (3x - 4) feet, and (6x - 4) feet. According to the problem, the sum of these lengths is 42 feet.
So, we can create the following equation:
(x - 4) + (3x - 4) + (6x - 4) = 42
Now, it's time to solve this equation to find the value of x.
Combining like terms, we have:
x - 4 + 3x - 4 + 6x - 4 = 42
Combining the x terms, we get:
10x - 12 = 42
Adding 12 to both sides of the equation, we have:
10x = 54
Dividing both sides by 10, we get:
x = 5.4
Since the lengths of the ropes are in whole numbers of feet, we can round x to the nearest whole number. In this case, x ≈ 5.
So, the lengths of the three ropes are:
x = 5 feet
(x + 3) = 8 feet
(x + 6) = 11 feet
Therefore, the lengths of the three ropes are 5 feet, 8 feet, and 11 feet.