Question 121331
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:
{{{(3x-4)+(3x+3-4)+(3x+6-4) = 42}}} Combine like-terms.
{{{9x-12+9 = 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.
{{{(15-4)+(18-4)+(21-4) = 11+14+17}}} = {{{42}}}