Question

a 13-foot piece of string is cut into two pieces so that the longer piece is 4 feet longer than twice the shorter piece. if the shorter piece is x feet long, find the lengths of both pieces.

Answer 1

The length of the longer piece is 10 foot and the length of the shorter piece is 3 foot.

Explanation:

Given:

let length of longer piece of string be y feet.

And length of shorter piece of string is x feet.

The total length of piece of string is 13 foot.

To Find;

x = ?

y = ?

Solution:

According to the first condition it is given that the longer piece is 4 feet longer than twice the shorter piece, when the string is cut in two pieces.

So numerically the longer piece will be given as

`y = 2x + 4` say equation number 1

Now given total length of the piece of string is 13 foot, that is the sum of shorter piece and longer piece. And numerically will be given as

`\textrm{total length of string} = \textrm{length of shorter piece + length of longer piece}\\13 = x + y\\13 = x + (2x +4)\ \textrm{from equation 1 we substituted the value}\\13 = 3x + 4\\3x = 9\\x = 3\\`

Which is the length of shorter piece of string.

Now substitute this x value in equation 1 we will get length of longer piece

`y = 2(3) + 4\\y = 6 + 4\\y = 10\\`

which is the length of longer piece

So, the length of shorter piece is 3 foot and the length of longer piece is 10 foot i.e in all it is 13 foot.