Question

14-yard fishing line is cut into two pieces. Three times the length of the longer piece is four times the length of the shorter piece. Find the length of each piece.

(Hint: Let x = smaller piece...)

Answer 1

The small piece is 6 yards and the large piece is 8 yards.

Explanation:

Let x = small

Let y = large

x + y = 14 3y = 4x

3y = 4x Divide both sides of the equation by 3 to solve for y

y =
`(4)/(3)` x Plug
`(4)/(3)` x in for y in the first equation above.

x + y = 14

x +
`(4)/(3)` x = 14 x and 1 x mean the same thing. Another name for 1 is
`(3)/(3)`

`(3)/(3)`x +
`(4)/(3)`x = 14

`(7)/(3)`x = 14 Multiple both sides by
`(3)/(7)` to solve for x

(
`(3)/(7)`)(
`(7)/(3)`x) = 14(
`(3)/(7)`) you can write 14 as
`(14)/(1)`(
`(3)/(7)`) =
`(42)/(7)`= 6

x = 6

If x = 6, then y must be 8 because 6 + 8 = 14