Linear / Rational / Variable Equations

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SAT Math › Linear / Rational / Variable Equations

Questions 1 - 10

1

Translate into an algebraic expression:

One third of the difference of a number and 3 equals five times the number.

$\frac{1}{3}\left ( x-3 \right )=5x$

$\frac{1}{3}x-3=5$

$\frac{1}{3}x-3=5x$

$\frac{1}{3}\left ( x+3 \right )= 5x$

$3\left ( x-3 \right )=5x$

Explanation

You have to form the difference first and must be enclosed in parentheses which gets multiplied by 1/3. The word "equals" means the "=" symbol

2

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

2

3

4

6

7

Explanation

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

3

Two cars start 25 mile apart and drive away from each other in opposite directions at speeds of 50 and 70 miles per hour. In approximately how many minutes will they be 400 miles apart?

None of the other answers

187.5

200

3.33

3.125

Explanation

The cars have a distance from each other of 25 + 120t miles, where t is the number of hours, 25 is their initial distance and 120 is 50 + 70, or their combined speeds. Solve this equation for 400:

25 + 120t = 400; 120t = 375; t = 3.125

However, the question asked for minutes, so we must multiply this by 60:

3.125 * 60 = 187.5 minutes.

4

If 5 + x is 5 more than 5,what is the value of 2_x_?

10

5

15

20

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

5

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

2

3

4

6

7

Explanation

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

6

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

$14$

$10$

$12$

$16$

$18$

Explanation

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

7

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?

$\$500$

$\$250$

$\$750$

$\$300$

$\$625$

Explanation

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

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

8

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?

$\$500$

$\$250$

$\$750$

$\$300$

$\$625$

Explanation

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

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

9

If 5 + x is 5 more than 5,what is the value of 2_x_?

10

5

15

20

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

10

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

$14$

$10$

$12$

$16$

$18$

Explanation

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

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