ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #43 : Linear / Rational / Variable Equations

Joy bought some art supplies.  She bought colored pencils for $1.25 per box and sketch pads for $2.25 each.  Joy bought one more sketch pad than colored pencil boxes and spent $9.25.  How many sketch pads did she buy?

Possible Answers:

2

4

3

5

1

Correct answer:

3

Explanation:

Let x = # of color pencil boxes and x+1 = # of sketch pads purchased.

So the equation to solve becomes 1.25x+2.25(x+1)=9.25

Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.

Example Question #321 : Algebra

\left | 2x - 3 \right |-x= 5

Possible Answers:

x=-8

x=8

x=-\frac{2}{3}

x=-8\ or \ x=-\frac{3}{2}

x=8\ or\ x=-\frac{2}{3}

Correct answer:

x=8\ or\ x=-\frac{2}{3}

Explanation:

This question deals with absolute value equations which will normally gives you two solutions.

You need to solve two sets of equations for absolute value problems:

2x-3 = x+5

and

2x-3=-\left ( x+5 \right )

Example Question #51 : Linear / Rational / Variable Equations

Steve sells cars.  His monthly salary is $1,000.  He gets a $500 commission for each car he sells.  If Steve wants to make $7,500 this month, how many cars would he have to sell?

Possible Answers:

Correct answer:

Explanation:

Let  = money earned and  = number of cars sold

So

 and solving shows that he needs to sell 13 cars to make $7,500.

Example Question #41 : Linear / Rational / Variable Equations

A chemistry student needs to dilute some acid.  How much pure water should be added to 2 gallons of 80% acid solution to yield 20% acid solution?

Possible Answers:

Correct answer:

Explanation:

Let pure water = 0 % and pure acid = 100%

The general equation to use is:

V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}  where is the volume and is the percent solution.

So the equation to solve becomes  and  gallons of pure water needs to be added to get a 20% acid solution.

Example Question #41 : How To Find The Solution To An Equation

The Widget Company makes widgets.  The monthly fixed costs are $750.  It costs $45 to make each widget.  The widgets sell for $75 a piece.

What is the monthly break-even point?

Possible Answers:

Correct answer:

Explanation:

The break-even point is where the costs equal revenue.

Let = # of widgets sold.

Costs: 

Revenue: 

So the equation to solve becomes

So the break-even point occurs when they sell 25 widgets.

Example Question #41 : Algebra

The Widget Company makes widgets.  The monthly fixed costs are $750.  It costs $45 to make each widget.  The widgets sells for $75 a piece.

The Widget Company wants to make a profit of $3,000.  How many widgets must be sold?

Possible Answers:

Correct answer:

Explanation:

Profits = Revenues - Costs

Revenue: 

Costs: 

Profit:

So the equation to solve becomes

So a $3,000 profit occurs when they sell 125 widgets

Example Question #211 : Algebra

Sally sells custom picture frames.  Her monthly fixed costs are $350.  It costs $10 to make each frame.  Sally sells her picture frames for $35 each.

How many picture frames must Sally sell in order to break even?

Possible Answers:

Correct answer:

Explanation:

The break-even point is where the costs equal the revenues.

Let  = # of frames sold

Costs: 

Revenues: 

Thus,

So 14 picture frames must be sold each month to break-even.

Example Question #321 : Algebra

Sally sells custom picture frames.  Her monthly fixed costs are $350.  It costs $10 to make each frame.  Sally sells her picture frames for $35 each.

To make a profit of $500, how many frames need to be sold?

Possible Answers:

Correct answer:

Explanation:

Let  = # of frames sold

Revenues: 

Costs: 

Profits =

So the equation to solve becomes

So 34 picture frames must be sold to make a $500 profit.

Example Question #41 : How To Find The Solution To An Equation

How much pure water must be added to 2 gallons of 90% pure cleaning solution to yield a 30% pure cleaning solution?

Possible Answers:

Correct answer:

Explanation:

Let pure water be 0% and pure solution be 100%.

So the general equation to solve is:

V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f} where  is the volume and the  is percent solution.

So the equation to solve becomes

Solving shows that we need to add 4 gallons of pure water to 2 gallons of 90% pure cleaning solution to get a 30% pure solution.

Example Question #322 : Algebra

Susan got a new piggy bank and counted the change she put into it.  She had one more nickel than dimes and two fewer quarters than nickles.  The value of her change was $1.40.  How many total coins did she have?

Possible Answers:

Correct answer:

Explanation:

Let  = number of dimes,  = number of nickels, and 

= number of quarters.

The general equation to use is:

V_{1}N_{1} + V_{2}N_{2} + V_{3}N_{3} = V_{f} where  is the money value and  is the number of coins

So the equation to solve becomes

Thus, solving the equation shows that she had five nickels, four dimes, and three quarters giving a total of 12 coins.

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