Question

A 5-foot rope is cut into 2 pieces. Seven less than three times the length of the longer rope piece x is five times the length of the shorter piece, which is (5 − x) ft. Find the length of the longer rope piece x (in ft)

Answer 1

Let's call the length of the longer rope piece x and the length of the shorter rope piece y. We know that:

x + y = 5 (the total length of the rope is 5 feet)

And from the problem statement, we have:

3x - 7 = 5y

Now we can use the first equation to solve for y:

y = 5 - x

Substituting this expression for y into the second equation:

3x - 7 = 5(5 - x)

Expanding the right side:

3x - 7 = 25 - 5x

Adding 5x to both sides:

8x - 7 = 25

Adding 7 to both sides:

8x = 32

Dividing both sides by 8:

x = 4

So the length of the longer rope piece is 4 feet.