### All ACT Math Resources

## Example Questions

### Example Question #1781 : Act Math

If the diameter of a car wheel is 1 foot, how many miles has the car gone after 3500 revolutions?

**Possible Answers:**

**Correct answer:**

The circumference of the tire is therefore pi, meaning that in 3500 revolutions the car will go 10,995.6 feet. Dividing by 5280 feet per mile yields 2.1 miles.

### Example Question #281 : Algebra

A chemistry student needs to dilute 1 L of 75%-acid solution. How much water should be added to yield a 25%-acid solution?

**Possible Answers:**

**Correct answer:**

where = volume and = percent

Pure water = 0% and pure acid = 100%

So the equation to solve becomes

or

So 2 L of pure water should be added to 1 L 75%-acid solution to yield 25%-acid solution.

### Example Question #291 : Algebra

The Teddy Bear Parade makes teddy bears. Their monthly fixed costs are $550. It costs $25 to make each bear and they sell for $50 each.

What is the monthly break-even point?

**Possible Answers:**

**Correct answer:**

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

Let = number of teddy bears sold

Revenue:

Costs:

So when Costs = Revenue we have the break-even point thus the equation to solve becomes or .

So to break-even, 22 teddy bears must be sold.

### Example Question #11 : Equations / Inequalities

The Teddy Bear Parade makes teddy bears. Their monthly fixed costs are $550. It costs $25 to make each bear and they sell for $50 each.

To make a profit of $750, how many teddy bears must be sold?

**Possible Answers:**

**Correct answer:**

Let = number of teddy bears sold.

Revenue:

Costs:

Profits = or

So the equation to solve becomes

So to make a profit of $750, 52 teddy bears must be sold.

### Example Question #11 : How To Find The Solution To An Equation

How much pure acid should be added to 1 L of 50%-acid solution to yield a 75%- acid solution?

**Possible Answers:**

**Correct answer:**

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

where = volume and = percent.

Let = amount of pure acid to add.

So the equation to solve becomes

Thus 1 L of 50%-acid solution added to 1 L of pure acid solution yields 2 L of 75%-acid solution.

### Example Question #11 : How To Find The Solution To An Equation

Charlie's Cookies sells desserts. Their monthly fixed costs are $350. It costs $10 to make a dozen cookies. They sell each dozen for $15.

How many cookies must be sold each month to break-even?

**Possible Answers:**

**Correct answer:**

The break-even point occurs when the revenues equal the costs.

Let = number of dozens of cookies sold.

:

:

to break-even.

So the equation to solve becomes

or

So 70 dozen cookies must be sold to break-even, thus cookies.

### Example Question #11 : Equations / Inequalities

Charlie's Cookies sells desserts. Their monthly fixed costs are $350. It costs $10 to make a dozen cookies. They sell each dozen for $15.

The company wants to make a profit of $500. How many dozens of cookies must be sold to reach their profit goal?

**Possible Answers:**

**Correct answer:**

Let = number of dozens of cookies sold.

So the equation to solve becomes .

So the company must sell 170 dozen cookies to make a $500 profit.

### Example Question #294 : Algebra

Mike and Joey live 215 miles apart. They meet at a campground between them. Mike drove 50 mph and Joey drove 60 mph and left one hour after Mike. How far did Mike travel?

**Possible Answers:**

**Correct answer:**

The distance Mike traveled plus the distance Joey traveled is the total distance between them.

Let = hours traveled

So the equation to sovle becomes

Thus hours traveled

So Mike traveled .

And Joey traveled .

### Example Question #12 : Linear / Rational / Variable Equations

What is the value of when ?

**Possible Answers:**

**Correct answer:**

Simply solve for by adding five to both sides and then dividing both sides by three to get by itself.

### Example Question #13 : Equations / Inequalities

By how much is the value of greater than the value of when and ?

**Possible Answers:**

**Correct answer:**

Input and into both equations. Solve them and then find the difference between the two answers.