ACT Math : Equations / Inequalities

Study concepts, example questions & explanations for ACT Math

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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:

2.1

50.1

3.5

13.5

10.2

Correct answer:

2.1

Explanation:

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:

Explanation:

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

Explanation:

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:

Explanation:

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:

Explanation:

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

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

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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

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