All ACT Math Resources
Example Questions
Example Question #13 : 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.
What is the monthly break-even point?
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 #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.
To make a profit of $750, how many teddy bears must be sold?
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 #15 : Equations / Inequalities
How much pure acid should be added to 1 L of 50%-acid solution to yield a 75%- acid solution?
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 #16 : 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.
How many cookies must be sold each month to break-even?
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 #292 : Algebra
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?
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 #18 : Equations / Inequalities
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?
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 #293 : Algebra
What is the value of when ?
Simply solve for by adding five to both sides and then dividing both sides by three to get by itself.
Example Question #20 : Equations / Inequalities
By how much is the value of greater than the value of when and ?
Input and into both equations. Solve them and then find the difference between the two answers.
Example Question #294 : 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?
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 #295 : Algebra
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?
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.
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