Robert's wire is [tex]1\frac{3}{7}[/tex] longer than Maria's wire
Let's say
Robert's wire = x
Maria's wire = y
From the problem given we know that:
[tex]\boxed {\frac{1}{2} x = \frac{2}{3}y }\\ \boxed {x + y = 10 }[/tex]
[tex]\boxed {x = 10-y }[/tex]
So we get two equations:
[tex]\boxed {\frac{1}{2} x = \frac{2}{3}y }\\\boxed {\frac{1}{2} (10-y) = \frac{2}{3}y } \\\boxed {5 - \frac{1}{2}y = \frac{2}{3} y }\\\boxed {5 = \frac{2}{3}y + \frac{1}{2}y }\\\boxed {5 = \frac{7}{6} y }\\\boxed { y= \frac{30}{7} }[/tex]
Let's subsitute the variable y into one of the equation above:
[tex]\boxed {x + y = 10 }\\\boxed {x + \frac{30}{7} = 10 }\\\boxed { x = 10 -\frac{30}{7} }\\\boxed { x = \frac{70-30}{7} }\\\boxed { x = \frac{40}{7} }[/tex]
Robert's wire (x) is [tex]\frac{40}{7}[/tex] feet long and Maria's wire is [tex]\frac{30}{7}[/tex] long.
The difference between Robert's and Maria's is
[tex]\boxed {= \frac{40}{7} - \frac{30}{7} }\\\boxed {= \frac{10}{7} }\\\boxed {= 1\frac{3}{7} }[/tex]
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Keywords: multi-step problem, fraction, part to whole relationship, mixed fraction, additional fraction, subtraction fraction from a whole number