### All ACT Math Resources

## Example Questions

### Example Question #291 : Algebra

Susan has one gallon of 25% acid solution, and she needs 75% acid solution for her experiment. How much pure acid should she add?

**Possible Answers:**

**Correct answer:**

Pure water is 0% and pure acid is 100%.

The general formula to use is , where is the volume and is the percent.

Our known values are listed below.

We will call our unknown added acid .

So the equation to solve becomes .

### Example Question #21 : How To Find The Solution To An Equation

Sally sells hair accessories. Her monthly fixed costs are $150. It costs her $5 to make each barrette, and she sells them for $10 each.

How many barrettes must Sally sell in order to break even with her costs?

**Possible Answers:**

**Correct answer:**

The break-even point occurs when the revenues are the same as the costs.

Let be the number of barrettes sold.

Revenue is equal to .

Cost is equal to .

The equation to solve becomes

Solving shows that 30 barrettes must be sold to break-even.

### Example Question #21 : How To Find The Solution To An Equation

Sally sells hair accessories. Her monthly fixed costs are $150. It costs her $5 to make each barrette, and she sells them for $10 each.

If Sally wants to make a profit of $250, how many barrettes must she sell?

**Possible Answers:**

**Correct answer:**

Let be equal to the number of barrettes sold.

Revenue will be equal to .

Costs will be equal to .

The equation to solve becomes .

To reach the profit goal of $250, we need to calculate the value of .

### Example Question #1791 : Act Math

What are the values for x that satisfy the equation (x-d)(x+c)=0?

**Possible Answers:**

d and c

dc

-dc

d and -c

–d and c

**Correct answer:**

d and -c

Set each component of this equation equal to zero and solve for *d *and *c. *

(x-d)(x+c)=0

x-d=0

d=0

x+c=0

x=-c

### Example Question #21 : How To Find The Solution To An Equation

If A + B = C and B *– *C = 3, what does A equal?

**Possible Answers:**

*–*3

3

*–*9

6

9

**Correct answer:**

*–*3

This question can be solved using substitution. There are several ways to subsitute, but one possible method is to substitue (A+B) for C in the equation B-C=3: B-(A+B)=3. This simplifies to (B-A-B=3) (don't forget to distribute the negative!). Since (B-B)=0, -A must equal 3 (-A=3). If we divide both sides by -1, A=-3. If you got an answer of positive 3, you may have forgotten to divide both sides by -1.

### Example Question #22 : How To Find The Solution To An Equation

The population of a bird species is modeled by the following equation:

,

where represents the number of years from the present. How many years will it take the population to reach 130 birds (rounded to the nearest tenth)?

**Possible Answers:**

280.8

12.2

38.5

23.0

20.4

**Correct answer:**

20.4

Plugging in 130 for P, the equation becomes 130 = (11/8)x + 102. Solving for x, we obtain x = 20.4 years.

### Example Question #1793 : Act Math

What is the value of c when 3c + 4 = 2c **–** 7?

**Possible Answers:**

0

**–**11

11

1

No Solution

**Correct answer:**

**–**11

First put the variables on one side by subtracting 2c on both sides to get c + 4 = –7. Then subtract the 4 on both sides to arrive at your answer, c = **–**11.

### Example Question #1792 : Act Math

If y=0.35(300 **– **2y), what is the value of y to the nearest tenth?

**Possible Answers:**

62.3

51.2

61.8

65.0

**Correct answer:**

61.8

Distributing the 0.35 to both the 300 and **–**2y leaves y=105 **– **0.7y

Adding 0.7y to both sides and dividing by 1.7 gives 61.8.

### Example Question #1794 : Act Math

Which of the lines below is not parallel to 4x **– **3y = 17 ?

**Possible Answers:**

–y= –(4/3)x – (17/3)

8x + 6y = 34

8x **–** 6y = 34

2x **–** 1.5y = 8.5

**Correct answer:**

8x + 6y = 34

For a line to be parallel with another, the slopes must be equal. All of the equations have a slope of 4/3 except 8x +6y=34.

### Example Question #21 : Linear / Rational / Variable Equations

If the expression x^{4} + 3cx **–** 2 is equal to 5 when x = **–**1, what is the value of c?

**Possible Answers:**

3

1

**–**2

2

**Correct answer:**

**–**2

Plugging in **–**1 into the equation for x and solving for c yields **–**2.