### All Algebra II Resources

## Example Questions

### Example Question #41 : Equations

Set up the equation: Two times a number is equal to one less than the number.

**Possible Answers:**

**Correct answer:**

Start by breaking up the details. Let be the unknown number.

Two times a number:

Is equal to:

One less than the number:

Combine all the terms.

The answer is:

### Example Question #42 : Setting Up Equations

Set up the following equation: Four times the quantity of two less than a number is eight times the number.

**Possible Answers:**

**Correct answer:**

To solve this question, break up the wording by parts.

Quantity of two less than a number:

Four times the quantity of two less than a number:

Is:

Eight times the number:

Combine the terms.

The answer is:

### Example Question #42 : Equations

A photo company charges a set-up fee to print photos and then per photo printed. Translate this into an expression.

**Possible Answers:**

**Correct answer:**

To translate this into an expression, it's helpful to identify what the constant is in the problem. In other words, what is not changing no matter how many photos you print? In this case, it's the set-up fee . Then, we identify where our variable will be coming into play. We don't know how many photos will be printed, so let's call the number of photos . We know that it costs per photo printed so that becomes . Add those together to get your final expression: .

### Example Question #43 : Equations

Set up an equation in terms of a single variable that can be used to solve the problem below.

The area of a rectangular pool is . The length of the pool is two feet less than twice the width. Find the dimensions of the pool.

**Possible Answers:**

None of the above

**Correct answer:**

The area of a rectangular is length times width. So,

If and . Then,

The length of the pool is two feet less than twice the width, which means:

Substitute in with :

so

### Example Question #41 : Setting Up Equations

Write the following equation:

Shirts are 15 dollars and jeans are 30 dollars.

The total amount of money you made from selling shirts and jeans is at least 200 dollars.

**Possible Answers:**

**Correct answer:**

You know that shirts sell for 15 dollars and jeans sell for 30 dollars.

The tricky part is knowing that you sold *at least* 200 dollars worth of merchandise.

This means that you could have sold more than 200 dollars, but no less than that.

This means that your answer is

### Example Question #41 : Equations

Corey buys potatoes for $2.25 per pound and quinoa for $5.75 per pound. If Corey buys *p* pounds of potatoes and *q* pounds of quinoa for $37.25, which of the equations below represents his transaction?

**Possible Answers:**

**Correct answer:**

The cost for *p* pounds of potatoes is 2.25*p* and the cost for *q* pounds of quinoa is 5.75*q*. The total amount Corey pays is the sum of the cost for potatoes and the cost for quinoa.

2.25*p* + 5.75*q* = 37.25

### Example Question #45 : Equations

Write in slope-intercept form

**Possible Answers:**

**Correct answer:**

Recall the form for slope-intercept as follows.

where represents the slope and is the y-intercept.

Given the equation in this question, first distribute the one fourth to both terms inside the parentheses.

Next, subtract two from both sides to isolate y.

This results in the slope-intercept form of the equation.

### Example Question #46 : Equations

Beetle A runs in a straight line for 30cm before bumping into Beetle B, who then runs for another 90cm at a rate 3 times faster than Beetle A.

What is the rate of Beetle B?

**Possible Answers:**

Unable to determine from the information provided

**Correct answer:**

Knowing:

**Beetle A: **

**Beetle B: **

**Combined:**

Multiply each term by LCD (3x) to get:

### Example Question #43 : Setting Up Equations

Set up the equation: The square root of six less than twice a number is equal to nine.

**Possible Answers:**

**Correct answer:**

Split up the sentence into parts.

Twice a number:

Six less than twice a number:

The square root of six less than twice a number:

Is equal to nine:

The answer is:

### Example Question #138 : How To Find F(X)

Set up the equation: The sum of two times a number and forty is equal to sixteen.

**Possible Answers:**

**Correct answer:**

Break up the problem into parts.

Two times a number:

The sum of two times a number and forty:

Is equal to sixteen:

Combine the terms to form the equation.

The answer is:

Certified Tutor

Certified Tutor