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Just to confirm one of your comments above -- "Yes, we can sum/subtract/multiply equations." -- would this be valid for the problem even if one of the equations didn't have any common variables. What I mean is, if the equations read:

Just to confirm one of your comments above -- "Yes, we can sum/subtract/multiply equations." -- would this be valid for the problem even if one of the equations didn't have any common variables. What I mean is, if the equations read:

Re: In the table above, what is the number of green marbles in J [#permalink]

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21 Nov 2014, 03:28

From the given table we could make equations like Equation 1. Given x+y=80 ----> x=80-y Equation2. Given y+z=120 Equation3. Given x+z = 160 Substituting the value of x in Equation 3 from Equation 1 Equation 4. (80-y)+z=160 ----> -y+z = 80 Adding Equation 2 and Equation 4 2z=200 ---> Z=100.

In the table above, what is the number of green marbles in Jar R ?

(A) 70 (B) 80 (C) 90 (D) 100 (E) 110

We can create three equations from the information presented in the table.

Equation 1: x + y = 80

Equation 2: y + z = 120

Equation 3: x + z = 160

These equations present us with a good opportunity to use the “combination method” to solve multiple equations. Here, we can add equations together. Because we need the number of green marbles in jar R, we need to determine the value of z.

We can start by multiplying equation 1 by -1.

-1(x + y = 80) = -x – y = -80

Next, we add this equation to equation 2. So we have:

-x - y = -80 + (z + y = 120) = z – x = 40

Now we can add z – x = 40 to equation 3. So we have:

–x + z = 40 + (x + z = 160)

2z = 200

z = 100

Answer D.
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