Consecutive Multiples?

Question

The lengths in feet of three ropes are consecutive multiples of 3. If each rope were 4 ft shorter, the sum of their lengths would be 42 ft.

Answer 1

15, 18, 21

15 + 18 + 21 = 54 - 12 = 42

Easiest way to think of this is that the middle rope is (42/3) = 14 + 4 = 18, then the other two are 3 less and 3 more.

Answer 2

3x, 3(x+1), 3(x+2) are three rope lengths of consecutive multiples of 3. If each rope was 4 feet shorter, then subtract 4 from each number, add them, and solve.

(3x-4) + [3(x+1) - 4] + [3(x+2) - 4] = 42
3x + 3x + 3 + 3x + 6 -12 = 42
9x - 3 = 42
9x = 45
x=5 (feet)

So the lengths are 3*5, 3*6, and 3*7 feet or
15, 18, and 21 feet

Answer 3

let the three ropes are: x,y,z
since they are consecutive multiples of 3, then:
x = x
y = x+3
z = y+3 = x+6
then,
(x-4)+(y-4)+(z-4)=42
(x-4)+(x+3-4)+(x+6-4)=42
(x-4)+(x-1)+(x+2)=42
3x-3=42
3x=45
x=15

x=15 then y = x+3 = 15+3 = 18; z = x+6 = 15+6 = 21.

So, the length of the ropes are: 15ft, 18ft, 21ft.

Answer 4

the lengths will be x, x+3, x+3+3 = x+6

so given
x-4 +x+3-4 + x+6 -4 = 42
or 3x -12 + 9 = 42
or 3x = 45
or x = 15

lengths are 15, 18, 21