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

Answer:

Robert's piece of wire is 5 feet long

and Maria's piece of wires is 7 feet long

Step-by-step 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".

$\frac{1}{2} x = \frac{2}{3} y$  --------------(1)

The total length of their wires is 12 feet.

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

=> $x=12-y$

Substitute x=12-y in equation (1)

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

$6-\frac{1}{2} y = \frac {2}{3} y$

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

$y=7$

Put y=7 in equation (2)

$x+7 = 12 \\x =5$