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?

Answers

Answer 1

Answer: 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)

Answer 2

Answer:

Robert's wire is $1(3)/(7)$ 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:

$\boxed {(1)/(2) x = (2)/(3)y }\n \boxed {x + y = 10 }$

$\boxed {x = 10-y }$

So we get two equations:

$\boxed {(1)/(2) x = (2)/(3)y }\n\boxed {(1)/(2) (10-y) = (2)/(3)y } \n\boxed {5 - (1)/(2)y = (2)/(3) y }\n\boxed {5 = (2)/(3)y + (1)/(2)y }\n\boxed {5 = (7)/(6) y }\n\boxed { y= (30)/(7) }$

Let's subsitute the variable y into one of the equation above:

$\boxed {x + y = 10 }\n\boxed {x + (30)/(7) = 10 }\n\boxed { x = 10 -(30)/(7) }\n\boxed { x = (70-30)/(7) }\n\boxed { x = (40)/(7) }$

Robert's wire (x) is $(40)/(7)$ feet long and Maria's wire is $(30)/(7)$ long.

The difference between Robert's and Maria's is

$\boxed {= (40)/(7) - (30)/(7) }\n\boxed {= (10)/(7) }\n\boxed {= 1(3)/(7) }$

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

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Final answer:

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Explanation:

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Answers

Answer:

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Step-by-step explanation:

Answer:

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What are Factors of a Number?

Numbers that divide an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal parts. A factor is a number that divides another number, leaving no remainder

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

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40 is the correct answer for this question.

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