ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors ibooks store

Example Questions

Example Question #121 : Algebra

In a group of 24 children, there are twice as many girls as there are boys.  How many boys are there?

Possible Answers:

8

16

14

12

10

Correct answer:

8

Explanation:

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 #122 : Gre Quantitative Reasoning

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?

Possible Answers:

$17,500,000

None of the other answers

$12,500,000

$20,000,000

$15,000,000

Correct answer:

$17,500,000

Explanation:

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 #122 : Algebra

For what value of x does 4(3x – 2) = 12?

Possible Answers:

5/6

2

2/3

5/3

1

Correct answer:

5/3

Explanation:

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 #121 : Algebra

If 11 + 3x is 29, what is 2x?

Possible Answers:

2

36

6

12

Correct answer:

12

Explanation:

First, solve for x:

11 + 3= 29

29 – 11 = 3x

18 = 3x

x = 6

Then, solve for 2x:

2= 2 * 6 = 12

Example Question #24 : How To Find The Solution To An Equation

If 2x = 3y = 6z = 48, what is the value of x * y * z?

Possible Answers:

1536

1024

3072

6144

2304

Correct answer:

3072

Explanation:

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

 

* y * z = 3072

Example Question #123 : Algebra

If 3|x – 2| = 12 and |y + 4| = 8, then |x - y| can equal ALL of the following EXCEPT:

Possible Answers:

2

18

10

6

14

Correct answer:

14

Explanation:

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 #31 : How To Find The Solution To An Equation

If is defined for all numbers  and  to be  x^2 - 2xy, then what is ?

Possible Answers:

Correct answer:

Explanation:

In evaluating, we can simply plug in 4 and 2 for  and  respectively. We then get .

Example Question #391 : Algebra

Translate into an algebraic expression:

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

Possible Answers:

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

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

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

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

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

Correct answer:

\frac{1}{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

Example Question #84 : Algebra

Translate into an algebraic expression:

Two fifths of the difference of five times a number and two equals six times the number.

Possible Answers:

Correct answer:

Explanation:

In order to translate the description into an algebraic expression, you must first form the difference , multiply it by , and then set the equation equal to , as follows:

 

Example Question #121 : How To Find The Solution To An Equation

A car averages  miles per gallon. If gas costs  per gallon, which of the following is closest to how much the gas would cost for this car to travel  typical miles?

Possible Answers:

Correct answer:

Explanation:

To solve this problem you should divide the total number of miles  by the miles per gallon , and then multiply by the cost of gas per gallon . This gives you , which is closest to .

Learning Tools by Varsity Tutors