Question

Half of Robert's piece of wire is equal to ⅔ of Maria's wire. The total length of their wires is 12 feet. How much longer is Robert's wire than Maria's?

Answer 1

Robert's piece of wire is 5 feet long

and Maria's piece of wires is 7 feet long

Explanation:

Suppose x and y are Robert's and Maria's piece of wires respectively.

We can write following equation using this statement "Half of Robert's piece of wire is equal to ⅔ of Maria's wire".

`(1)/(2) x = (2)/(3) y` --------------(1)

The total length of their wires is 12 feet.

`x+y=12` ------------(2)

=>
`x=12-y`

Substitute x=12-y in equation (1)

`\frac {1}{2} (12-y) = (2)/(3) y`

`6-(1)/(2) y = \frac {2}{3} y`

`6 = \frac {2} {3} y + \frac {1} {2} y`

`y=7`

Put y=7 in equation (2)

`x+7 = 12 \\x =5`