Answer:
let x be the Robert piece
y Maria's piece
x+y=10
0,5*x ( half of Robert piece)= 2/3 y( 2 thirds)
2 equations then
x+y= 10 then x= 10-y
0,5x= 0,67 y then we replace x by 10-y on the second equation and it gives
0,5(10-y)= 5-0,5y=0,67y
5= 1,17 y so y= 4,27 and then x= 10-y= 5,73
the question asks how much Robert wire is longer than Maria's wire
so we get x-y= 1,46
Robert's wire is longer [tex]\frac{4}{3}[/tex] times than Maria's wire and also it [tex]\frac{10}{7}[/tex] longer than Maria's wire
A wire is a single, usually cylindrical, flexible strand or rod of metal. It are used to bear mechanical loads or electricity and telecommunications signals.
Half of Robert's wire = 2 thirds of Maria's wire, so
[tex]\frac{1}{2} *[/tex] Robert's wire = [tex]\frac{2}{3} * Maria's wire[/tex]
The total length of their wires = 10 feet
10 feet = Robert's wire + Maria's wire
10 feet = [tex]\frac{4}{3} * Maria's wire[/tex] + Maria's wire
10 feet = [tex]\frac{7}{3} * Maria's wire[/tex]
Maria's wire = [tex]\frac{30}{7}[/tex] feet
[tex]\frac{1}{2} *[/tex] Robert's wire = [tex]\frac{2}{3} * Maria's wire[/tex]
Robert's wire = [tex]\frac{4}{3} * \frac{30}{7} [/tex]
Robert's wire = [tex]\frac{120}{21} feet[/tex]
Robert's wire = [tex] \frac{40}{7} feet[/tex]
If we draw the piece, we get the information that
7 units = 10 feet
1 unit = [tex]\frac{10}{7}[/tex] feet
Hence the Robert's wire is [tex]\frac{10}{7}[/tex] longer than Maria's wire because
Robert's wire - Maria's wire = [tex]\frac{40}{7} - \frac{30}{7} feet = \frac{10}{7} feet[/tex]
Grade: 5
Subject: math
Chapter: wire
Keywords:
wire, feet, piece of wire, piece, wires
