ACT Math : Equations / Inequalities

Study concepts, example questions & explanations for ACT Math

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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:

Explanation:

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

The general formula to use is V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}, 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:

Explanation:

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:

Explanation:

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

Explanation:

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

Explanation:

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

Explanation:

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

Explanation:

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

Explanation:

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

Explanation:

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 x4 + 3cx  2 is equal to 5 when x = 1, what is the value of c? 

Possible Answers:

3

1

2

2

Correct answer:

2

Explanation:

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

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