### All Algebra II Resources

## Example Questions

### Example Question #61 : Setting Up Equations

Billy donates two goats for every ten goats he buys from the farm. What is the equation that best represents this scenario? Let be goats, and be the total of goats Billy will have donated.

**Possible Answers:**

**Correct answer:**

If Billy buys 10 goats, he will have donated 2 goats.

If Billy buys 20 goats, he will have donated 4 goats.

We can set up the equation by finding the slope of the two points and .

Write the slope-intercept equation.

Substitute the known slope and a given point.

Write the equation.

Rewrite the equation in terms of and . The total will be the dependent variable.

The correct answer is:

### Example Question #62 : Setting Up Equations

Set up the equation: The product of negative two and five less than twice a number is six.

**Possible Answers:**

**Correct answer:**

Split up the sentence into parts.

Twice a number:

Five less than twice a number:

The product of negative two and five less than twice a number:

Is six:

Combine the terms.

The answer is:

### Example Question #63 : Setting Up Equations

The first two scores on a student's exams in an algebra class were and . What is the minimum score he should attempt to achieve on his third exam if he wants an average test score of at least ?

**Possible Answers:**

**Correct answer:**

Let be the desired minimum score the student needs to achieve on his third exam. If he wants his overall average test score to be or more, the following inequality will express the relationship between each of his scores so far, his desired average score, and :

Multiplying both sides of the inequality by yields

Adding like terms of the left-hand side of the inequality yields

Subtracting from both sides of the inequality yields

.

Hence, the student needs to achieve a score of at least on his next exam in order to achieve a test average of .

### Example Question #64 : Setting Up Equations

Set up the following equation: The difference of twice a number and the cube root of twice the number is ten.

**Possible Answers:**

**Correct answer:**

Break up the sentence into parts.

Twice a number:

The cube root of twice the number:

The difference of twice a number and the cube root of twice the number:

Is ten:

Combine the parts to form the equation.

The answer is:

### Example Question #65 : Setting Up Equations

Set up the equation: Three times the square root of twice a number is forty.

**Possible Answers:**

**Correct answer:**

Break up the sentence into parts. Work the terms of the square root first.

Twice a number:

The square root of twice a number:

Three times the square root of twice a number:

Is forty:

Combine the terms to set up the equation.

The answer is:

### Example Question #66 : Setting Up Equations

Set up the equation: Five less than eight times a number is fourteen.

**Possible Answers:**

**Correct answer:**

Break up the sentence into parts.

Eight times a number:

Five less than eight times a number:

Is fourteen:

The answer is:

### Example Question #67 : Setting Up Equations

Suppose Billy makes an hour, works eight hours a day, five days a week. Set up an equation that represents how much Billy makes on a weekly basis. Let be the total and be weeks.

**Possible Answers:**

**Correct answer:**

Determine how much Billy will earn per day. Since he works eight hours a day, multiply the hourly wage with the hours.

He will make 24 dollars a day.

For five days:

Billy will make 120 dollars per week.

Set up the equation.

The answer is:

### Example Question #68 : Setting Up Equations

Set up the equation: Six times the quantity of three less than twice a number is eleven.

**Possible Answers:**

**Correct answer:**

Break up the sentence into parts. Start by the inner quantity.

Three less than twice a number:

Six times the quantity of three less than twice a number:

Is eleven:

Combine the parts to form the equation.

The answer is:

### Example Question #69 : Setting Up Equations

Set up the equation: Four less than seven times a number is eighty.

**Possible Answers:**

**Correct answer:**

Break up the sentence into parts.

Seven times a number:

Four less than seven times a number:

Is eighty:

Combine the parts.

The answer is:

### Example Question #70 : Setting Up Equations

Set up the equation: Eight less than twenty times a number is nine.

**Possible Answers:**

**Correct answer:**

Split the sentence into parts.

Twenty times a number:

Eight less than twenty times a number:

Is nine:

Combine the terms.

The equation is:

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