### All Algebra II Resources

## Example Questions

### Example Question #31 : Equations

Solve the equation:

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

To solve the equation for *x*, simplify.

To remove the absolute value, we do the following:

From there, we simplify both equations until we are left with *x* by itself on the left side.

There, you have the solutions for *x*.

### Example Question #32 : Equations

Evaluate the expression for the given value of the variable.

**Possible Answers:**

-22

14

16

None of these answers are correct.

0

**Correct answer:**

16

To solve the expression, simply plug in the given value for *x*.

1.

2.

3.

4.

5.

Note: at step 1, don't forget that squaring a negative number yields a positive number, because (-) * (-) = (+), while cubing a negative number yields a positive number, because (+) * (-) = (-).

### Example Question #33 : Equations

A hot air balloon takes off from a location 17 feet above sea level, and rises at a rate of 30 feet per minute. Which of the following equations correctly models the hot air balloon's elevation *h** *(feet) as a function of time *t* (minutes)?

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

Remember, when a question says something like "*h* as a function of *t*", it means that *h* is dependent on the value of *t. *This means the equation would take the form *y=mx+b*, and *h* would take the place of *y*, the dependent variable, while *t *would take the place of *x*, the independent variable. This eliminates answer choices that have *t* in the dependent variable spot and *h* in the independent variable spot.

Next, the value for *m* in our new equation, *h=mt+b*, would be the rate of change (also known as the slope). The rate of change we're given in the problem is 30 feet per minute (the feet **per** minute tells you that this is a rate of change).

Finally, the value for *b* is the y-intercept (or in our case, the h-intercept). It is the starting value for our equation (when *t = 0*). The starting value we're given in the problem is 17 feet.

Therefore, the correct equation to model the hot air balloon is

### Example Question #34 : Equations

Simplify the following rational expression. State any restrictions on the variable.

**Possible Answers:**

**Correct answer:**

Before we simplify the expressions, let's determine any restrictions that may be in place. Restrictions are where the denominator equals 0. Our expression has as the denominator. The denominator equals 0 when , so we know we have at least one restriction at .

Now, we can simplify the expression. First, we factor the numerator.

Now, our expression is this:

Therefore, our expression simplifies to . There are no more restrictions in place with the simplified version, so the only restrictions we have are that . Our answer is

### Example Question #35 : Equations

Maria bought pens and a candy bar. The candy bar cost and her total bill came to . Which of the following equations can help you to find the cost of each pen?

**Possible Answers:**

**Correct answer:**

To express this situation we would have the following general form.

For our case, let be the price of each pen, which is the unknown.

Then, since we bought pens, the cost of pens would be .

Additionally, we spent on the candy bar.

The total cost of the purchase was .

Usually the total is by itself on one side of the equals sign.

Thus, we have that the equation is .

### Example Question #36 : Equations

Joe wants to start saving up money for college. He plans on saving of his total income, plus an additional per month. Which of the following is a correct equation describing the amount of money saved () based on total monthly income ()?

**Possible Answers:**

Not enough information provided.

**Correct answer:**

The equation must be set up so that the amount saved is dependent upon total income, ; Joe will set aside 5% of the money he makes for savings. We represent this algebraically as:

Next, we see that no matter how much money Joe makes, he plans to always set aside $65 per month for savings. This is called a *constant* because it doesn't matter how his total income varies, the $65 remains constant. We complete the expression for Joe's savings with this constant term, leaving us with:

The above expression is equivalent to Joe's savings, which we represent with the variable , so we create our equation:

### Example Question #37 : Equations

Matt and Patrick are brothers; Matt is five years less than twice Patrick's age. Which of the following equations correctly describes Matt's age relative to Patrick's age ?

**Possible Answers:**

The relationship cannot be expressed with the information given.

**Correct answer:**

The relationship can be described using multiplication by a factor of 2 (i.e. *twice* Patrick's age) and subtraction by 5 (i.e. 5 years *less)*; the subtraction does *not *take place inside of parentheses because it is Matt's age that is 5 years less and not Patrick's (which is represented by the variable ). Therefore, the equation describing the relationship between the brothers' ages is:

### Example Question #38 : Equations

Suppose a dollar is split using pennies and quarters. There are a total of 35 coins. Set up the equation, or equations, that will determine the amount of pennies and quarters used to divide the dollar. Use the variables and to represent pennies and quarters, respectively.

**Possible Answers:**

**Correct answer:**

The dollar amount is . Pennies are , and quarters are . Two equations will need to be used to solve for the amount of pennies and quarters to make up the dollar.

The first equation sums up the total of coins used. The total of pennies and quarters must add up to 35 coins.

The second equation uses the denominations of the pennies and quarters that sum up to the dollar. Write the equation.

These are the two equations needed to solve for .

The answer is:

### Example Question #39 : Equations

Set up the equation that best matches: Twice a number is two less than the number.

**Possible Answers:**

**Correct answer:**

To set up this equation, we must break down the statement into parts.

Let be the number.

Twice a number:

Is:

Two less than the number:

Combine the parts.

The answer is:

### Example Question #40 : Equations

Set up the equation: Three times a number is two less than twice the number.

**Possible Answers:**

**Correct answer:**

In order to set up this equation, we will need to break up the sentence statement into parts. Let the unknown number be .

Three times a number:

Is:

Two less than twice the number:

Combine the parts together.

The correct answer is:

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