Answered

IDNLearn.com is the place where your questions are met with thoughtful and precise answers. Discover comprehensive answers to your questions from our community of experienced professionals.

half of Robert's piece of wire is equal to 2 thirds of Maria's wire. The total lenght of their wire is 10 feet. How much longer is Robert's wire than Maria's?

Sagot :

CatieSlotzidn
You have a system of equations here. R=Robert's piece of wire M=Maria's piece of wire

R/2=2M/3
and
R+M=10

With some basic algebra, you can make that first equation into
R=4M/3
then use substitution to get
(4M/3)+M=10
Then solve for M
(4M/3)+(3M/3)=10
7M/3=10
7M=30
M=30/7

so Maria's wire is 30/7 feet long. With a little more substitution, we can get:
R+(30/7)=10
R=10-(30/7)
R=(70/7)-(30/7)
R=40/7 feet long

So your final answer would be that Robert's wire is 10/7 feet longer than Maria's (which you could always put into decimal form)
Evadin2019idn

Robert's wire is [tex]1\frac{3}{7}[/tex] longer than Maria's wire

Further Explanation

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]

Learn More

Multistep problem https://brainly.com/question/2954322

Multistep problem brainly.com/question/78097991

Mixed fraction brainly.com/question/745462

Keywords: multi-step problem, fraction, part to whole relationship, mixed fraction, additional fraction, subtraction fraction from a whole number

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.