### All ACT Math Resources

## Example Questions

### Example Question #71 : The Number System

If Exam 1 is worth 25% of the total grade, Exam 2 is worth 25% and Exam 3 is worth 50%, what is Dave’s final grade?

**Possible Answers:**

85.75

82

83.5

79

84

**Correct answer:**

84

Final Grade = Exam1 * 0.25 + Exam 2 * 0.25 + Exam3 * 0.50 =

96*0.25 + 70*0.25 + 85*0.5 =

24 + 17.5 + 42.5 = 84

### Example Question #1 : How To Multiply Decimals

A chemistry students needs to dilute some acid. How much water should be added to 2 L of 80% acid solution to yield 50% acid solution?

**Possible Answers:**

2.0 L

1.2 L

1.0 L

1.5 L

0.8 L

**Correct answer:**

1.2 L

Pure water would be 0% solution and pure solution would be 100%

V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}

Let x = amount of water to add

x(0) + 2(0.80) = (x + 2)(0.50) which when solved gives x = 1.2 L

### Example Question #13 : Problem Solving

Kevin is looking at the blueprint of the house he is building. The scale is 1 inch = 5 feet. On paper, the master bedroom is 2.5 inches by 3 inches. What is the actual size of the bedroom?

**Possible Answers:**

10 ft x 10 ft

7.5 ft x 9 ft

15 ft x 25 ft

12.5 ft x 15 ft

20 ft x 30 ft

**Correct answer:**

12.5 ft x 15 ft

The given dimensions must be multiplied by 5, so 2.5 inches becomes 12.5 feet, and 3 inches becomes 15 feet.

### Example Question #13 : Other Decimals

If , approximately how many inches are in one meter?

**Possible Answers:**

**Correct answer:**

and

Using the factor-label method we get the following equation.

We treat the units as if they are numbers, and can cancel the units from the fractions.

### Example Question #15 : Other Decimals

A car has gas mileage of 46 miles per gallon. Assume that gas costs $3.90 per gallon. What would be the total cost of gas if the car traveled 1,150 miles?

**Possible Answers:**

$179.40

$125.70

$100.00

$115.60

$97.50

**Correct answer:**

$97.50

First find out how many gallons of gas the car consumed while traveling 1150 miles. This can be found out like so:

1150 miles x ^{gallons}/_{46 miles }= 25 gallons

Multiplying 25 by $3.90 yields $97.50.

### Example Question #14 : Other Decimals

Evaluate

**Possible Answers:**

**Correct answer:**

First,

Then,

### Example Question #4 : How To Multiply Decimals

You bought a dozen eggs marked at and received change from . What is the percent of sales tax?

**Possible Answers:**

**Correct answer:**

Set the equation up as

Solve for , which equals

or

Therefore the percent sales tax is:

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