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Students use dowel rods to learn about equations. They lay several rods, some of which are red and some of which are white, end to end. The length of each red rod is [tex]$R$[/tex] centimeters, and the length of each white rod is [tex]$W$[/tex] centimeters. The students determine that the total length of 2 red rods and 7 white rods is the same as the total length of 4 red rods and 3 white rods.

Based on this relationship, which of the following equations must be true?

A. [tex]R=2W[/tex]
B. [tex]R=3W[/tex]
C. [tex]3R=5W[/tex]
D. [tex]7R=9W[/tex]
E. [tex]9R=7W[/tex]



Answer :

GinnyAnswer
To find the correct equation based on the given problem, we start by formulating the relationship from the information provided:

The length of each red rod is [tex]\( R \)[/tex] centimeters, and the length of each white rod is [tex]\( W \)[/tex] centimeters. We are told that:

[tex]\[ \text{The total length of 2 red rods and 7 white rods} = \text{The total length of 4 red rods and 3 white rods} \][/tex]

Mathematically, this can be written as:

[tex]\[ 2R + 7W = 4R + 3W \][/tex]

Next, we want to solve this equation for [tex]\( R \)[/tex] in terms of [tex]\( W \)[/tex].

First, subtract [tex]\( 2R + 3W \)[/tex] from both sides of the equation:

[tex]\[ 2R + 7W - (2R + 3W) = 4R + 3W - (2R + 3W) \][/tex]

Simplify both sides:

[tex]\[ 2R + 7W - 2R - 3W = 4R + 3W - 2R - 3W \][/tex]
[tex]\[ 4W = 2R \][/tex]

Now, divide both sides by 2 to solve for [tex]\( R \)[/tex]:

[tex]\[ 2W = R \][/tex]

So, the relationship between [tex]\( R \)[/tex] and [tex]\( W \)[/tex] is:

[tex]\[ R = 2W \][/tex]

Therefore, the correct equation that must be true is:

[tex]\[ R = 2W \][/tex]

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