GRE Math : How to find the solution to an equation
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Example Questions
Example Question #21 : Algebra
In a group of 24 children, there are twice as many girls as there are boys. How many boys are there?
14
8
12
10
16
8
Since there are twice as many girls as boys, we know that 2b = g.
Since there are 24 total, we know that b + g = 24.
Substituting the first equation into the second equation yields
b + 2b = 24
3b = 24
b = 8
Example Question #81 : Linear / Rational / Variable Equations
For each megawatt of power that it produces, a power plant spends $30,000 on coal, $50,000 on salaries, and $20,000 on general expenses. If the plant produces 250 megawatts, how much does it spend on salaries and general expenses combined?
$17,500,000
$20,000,000
$12,500,000
$15,000,000
None of the other answers
$17,500,000
The problem is simple if you do not mix up your values and their meanings. What we know is that for 250 megawatts, we should have 250 times the expenses in each of our categories. Therefore, for our data, we know the following.
For salaries, we have $50,000 * 250 or $12,500,000.
For general expenses, we have $20,000 * 250 or $5,000,000
Therefore, our total is: $12,500,000 + $5,000,000 = $17,500,000
We also could have calculated this by adding $50,000 and $20,000 together to get $70,000 per megawatt. This would be $70,000 * 250 = $17,500,000 as well.
Example Question #21 : Algebra
12
6
20
24
2
24
Example Question #82 : Linear / Rational / Variable Equations
For what value of x does 4(3x – 2) = 12?
5/6
5/3
2
1
2/3
5/3
We have to solve the equation 4(3x – 2) = 12. First, we can distribute the left side.
4(3x) – 4(2) = 12
12x – 8 = 12
Then we add 8 to both sides.
12x = 20
Divide both sides by 12.
x = 20/12
Simplify 20/12 by dividing the numerator and denominator by 4.
x = 20/12 = 5/3
The answer is 5/3.
Example Question #83 : Linear / Rational / Variable Equations
If 11 + 3x is 29, what is 2x?
36
2
12
6
12
First, solve for x:
11 + 3x = 29
29 – 11 = 3x
18 = 3x
x = 6
Then, solve for 2x:
2x = 2 * 6 = 12
Example Question #23 : Algebra
If 2x = 3y = 6z = 48, what is the value of x * y * z?
2304
1024
6144
1536
3072
3072
Create 3 separate equations to solve for each variable separately.
1) 2x = 48
2) 3y = 48
3) 6z = 48
x = 24
y = 16
z = 8
x * y * z = 3072
Example Question #61 : How To Find The Solution To An Equation
If 3|x – 2| = 12 and |y + 4| = 8, then |x - y| can equal ALL of the following EXCEPT:
2
6
10
18
14
14
We must solve each absolute value equation separately for x and y. Remember that absolute values will always give two different values. In order to find these two values, we must set our equation to equal both a positive and negative value.
In order to solve for x in 3|x – 2| = 12,
we must first divide both sides of our equation by 3 to get |x – 2| = 4.
Now that we no longer have a coefficient in front of our absolute value, we must then form two separate equations, one equaling a positive value and the other equaling a negative value.
We will now get x – 2 = 4
and
x – 2 = –4.
When we solve for x, we get two values for x:
x = 6 and x = –2.
Do the same thing to solve for y in the equation |y + 4| = 8
and we get
y = 4 and y = –12.
This problem asks us to solve for all the possible solutions of |x - y|.
Because we have two values for x and two values for y, that means that we will have 4 possible, correct answers.
|6 – 4| = 2
|–2 – 4| = 6
|6 – (–12)| = 18
|–2 – (–12)| = 10
Example Question #1 : How To Find The Equation Of A Perpendicular Line
If a line has an equation of 
Putting the first equation in slope-intercept form yields 
A perpendicular line has a slope that is the negative inverse. In this case, 
Example Question #26 : Linear / Rational / Variable Equations
No solutions.
No solutions.
Cross multiplying leaves 
Example Question #31 : Linear / Rational / Variable Equations
If 
In evaluating, we can simply plug in 4 and 2 for 
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