### All ACT Math Resources

## Example Questions

### Example Question #71 : How To Find The Solution To An Equation

How much water should be added to of 90% cleaning solution to yield 50% cleaning solution?

**Possible Answers:**

**Correct answer:**

Pure water is 0% and pure solution 100%. Let = water to be added.

in general where is the volume and is the percent.

So the equation to solve becomes

and

### Example Question #72 : How To Find The Solution To An Equation

Solve and

**Possible Answers:**

**Correct answer:**

This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of to get and then substutite the into the second equation to get

.

Solving this equation gives and substituting this value into one of the original equations gives , thus the correct answer is .

### Example Question #73 : How To Find The Solution To An Equation

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:**

**Correct answer:**

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

So the equation to solve becomes .

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

### Example Question #74 : How To Find The Solution To An Equation

**Possible Answers:**

**Correct answer:**

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:

and

### Example Question #141 : Algebra

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:**

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 #123 : Equations / Inequalities

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:**

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

The general equation to use is:

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 #141 : Algebra

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:**

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 #81 : 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 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:**

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 #141 : 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:**

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 #145 : 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:**

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.

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