# GRE Math : Linear / Rational / Variable Equations

## Example Questions

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### Example Question #111 : Linear / Rational / Variable Equations

Ben is walking three dogs that weigh an average of 75 pounds each. Ben begins to walk a fourth dog, and the average weight of the dogs decreases to 70 pounds. What is the weight in pounds of the fourth dog?

Explanation:

The total weight of the first three dogs is 225 pounds. This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:

Pets Plus makes bird houses.  Their monthly fixed expenses are $750. The cost for each bird house is$15.  The bird houses sell for $40. What is the monthly break-even point at Pets Plus? Possible Answers: Correct answer: Explanation: Let the number of bird houses sold each month. The break-even point is where the revenue is the same as the costs: Solve for : Therefore, Pets Plus must sell 30 bird houses to break-even. ### Example Question #113 : Linear / Rational / Variable Equations Pets Plus makes bird houses. Their monthly fixed expenses are$750.  The cost for each bird house is $15. The bird houses sell for$40.

If Pets Plus sells 50 bird houses, what is the profit?

Explanation:

Let  = the number of birdhouses sold each month.

Substituting in 50 for  gives an answer of 500, so the profit on 50 birdhouses is \$500.

### Example Question #114 : Linear / Rational / Variable Equations

George is three times older than Joey.  The sum of their ages is 16.  What is the product of their ages?

Explanation:

Let  = Joey's age and  = George's age.

Then the equation to solve becomes .

Therefore, Joey is 4 years old and George is 12 years old, so the product of their ages is 48.

### Example Question #115 : Linear / Rational / Variable Equations

Three consecutive even numbers add to 42.  What is the middle number?

Explanation:

Let  = 1st even number, = 2nd even number, and  = 3rd even number.

Then the equation to solve becomes .

Thus , so the middle number is 14.

### Example Question #116 : Linear / Rational / Variable Equations

Consider the following equation:

Which of the following must be true?

Explanation:

The quantity inside the absolute value brackets must equal either  or , depending on whether the quantity inside the brackets is positive or negative. We therefore have two seperate equations:

To solve the first equation, add 9 to both sides:

Subtract  from both sides:

This is the first solution. Now let's look at the second equation. The distributive law gives us:

Divide both sides by 3:

Therefore, is either 4 or 6.

Statement  does NOT have to be true because  can also equal 4.

Statement  must be true because both 4 and 6 are positive .

Finally, statement  always holds because 4 and 6 are both even.

### Example Question #117 : Linear / Rational / Variable Equations

If

,

then

Explanation:

Divide both sides by 300 to get .  Subtract 7 and divide by two to get .

### Example Question #118 : Linear / Rational / Variable Equations

If b – 3 = a, then (a – b)2 =

The answer cannot be determined from the given information.

–9

3

–3

9

9

Explanation:

The quantity can be regrouped to be –3 = a – b.  Thus, (a – b)2 = (–3)2 = 9.

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