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Practical Peter was asked to cut a 99 foot rope into three smaller, equal length ropes.

However, as usual, Pete couldn't find his measuring tape so he guessed!

When he finally did find his tape (it was under his hat), he discovered that:

A) the second piece of rope was twice as long as the first piece, minus 35 feet (i.e. 2 x first, - 35).
B) the third piece of rope was half the length of the first, plus 15 feet (i.e. 0.5 x first, + 15)

How long were each of the pieces of rope?

First  = 34 feet.
Second = 33 feet.
Third  = 32 feet.

This question can be solved easily using algebra, if we call the length of the first rope A, we have:

Rope 1 = A
Rope 2 = 2 x A - 35
Rope 3 = 1 ÷ 2 x A + 15

The three ropes add to 99 feet, so:

99 = Rope 1 + Rope 2 + Rope 3

99 = A + (2 x A - 35) + 1 ÷ 2 x A + 15

99 = 3.5 x A - 20

Adding 20 to both sides we have:

119 = 3.5 x A

So:

A = 119 ÷ 3.5

A = Rope 1 = 34 feet
Rope 2 = 2 x 34 - 35 = 68 - 35 = 33 feet
Rope 3 = 1 ÷ 2 x A + 15 = 1 ÷ 2 x 34 + 15 = 17 + 15 = 32 feet

Just to check:

Rope 1 + Rope 2 + Rope 3 = 34 + 33 + 32 = 99.

As required. QED.

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