# Algebra II : Setting Up Expressions

## Example Questions

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### Example Question #1 : Setting Up Expressions

Carla wants to sell stickers to advertise her website. The machine that makes stickers costs $22, and each sticker costs$2 to make. She plans to sell these stickers for $3 each. Write an equation that describes the number of stickers Carla would have to sell in order to break even. Possible Answers: Correct answer: Explanation: Here, we can see that the independent variable is the number of stickers, so we'll call that . Each sticker costs$2 to make, so we'll write that as . The cost of the machine is always the same ($22), so we call that a constant. So far, we have as the cost of making number of stickers. Now, we need to describe the revenue gained by selling number of stickers. We know that Carla wants to sell the stickers at$3 each, which we can write as .

"Breaking even" means that your costs equal your income. In other words, it's the point at which Carla's sold exactly enough stickers to make all of her initial investment back. In math, we use an equal sign to describe this. Hence, we end up with the equation:

### Example Question #2 : Setting Up Expressions

Sally has 3 dollars saved. She works at the ice cream shop where she earns 5 dollars an hour. How many hours does she need to work to have enough money to buy a doll that is 23 dollars?

Explanation:

To set up this equation we need to put the amount of money she needs on one side of the equation and the amount of money she earns on the other side of the equation. It looks like the following

where  represents the number of hours Sally works. To get the dollar amount she earns for the hours she works, we mulitply it by 5.  The 3 represents the amount of money she already has saved. These two added together needs to equal 23 dollars, the amount for the doll.

From here we solve for :

### Example Question #3 : Setting Up Expressions

Set up the expression to solve the following word problem:

Annie, Josh, and Brenda each have a certain number of cards. Josh has twice as many cards as Annie, and Brenda has three times as many cards as Josh. They have  cards in total.

Explanation:

Let us call the number of cards Annie has

Josh has twice as many so we can call the number of cards Josh has

Brenda has 3 times as many cards as Josh so we can call the number of cards Brenda has

The total is 90 so we have

Which we simplify by adding all the x terms:

### Example Question #4 : Setting Up Expressions

A car dealer receives  commission on his total sales amount when he sells less than  cars per month. If he sells over  cars per month, he receives  commision.

If each cars sells for , which expression set correctly repressent the salesman's earnings per month,  and the amount of cars sold, ?

or

or

or

Explanation:

The salesman will sell either more than 5 cars or less than 5.

Therefore, only one set of the equations will be true for any one month.

The word between the expressions needs to be "or."

The total profit is expressed by 30,000x.

The commision can be calculated as .

The higher commision must be matched to the equation for greater amount of cars sold,

### Example Question #1 : Expressions

We have three cats, Chai, Sora, and Newton. Chai is 3 years old. Sora two years older than twice Chai's age. Newton is one year younger than one-fourth of Sora's age. How old are Sora and Newton?

Sora: 3 years

Newton: not born yet

Sora: 1 year

Newton: 8 years

Sora: 5 years

Newton: 6 years

Sora: 4 years

Newton: one half year

Sora: 8 years

Newton: 1 year

Sora: 8 years

Newton: 1 year

Explanation:

To make this much easier, translate the word problem into a system of three equations.

We have C for Chai, S for Sora, and N for Newton. To find Sora's age, plug in  into .

Sora is 8 years old. Use this to find Newton's age.

Newton is one year old.  So the answer is:

Sora, 8 years

Newton, 1 year

### Example Question #1 : How To Find The Missing Number In A Set

The sum of three consecutive even integers equals 72. What is the product of these integers?

13800

13728

10560

12144

17472

13728

Explanation:

Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.

x + (x + 2) + (x + 4) = 72

3x + 6 = 72

3x = 66

x = 22.

This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.

The answer is 13728.

### Example Question #5 : Setting Up Expressions

Express as a mathematical expression.

more than

Explanation:

Take every word and translate into math.

more than means that you need to add  to something.

That something is  so just combine them to have an expression of

### Example Question #6 : Setting Up Expressions

Express as a mathematical expression.

less than

Explanation:

Take every word and translate into math.

less than means that you need to subtract  from something.

That something is  so just combine them to have an expression of

### Example Question #7 : Setting Up Expressions

Express as a mathematical expression.

times

Explanation:

Take every word and translate into math.

times something means that you need to multiply  to something.

That something is  so just combine them to have an expression of

### Example Question #8 : Setting Up Expressions

Express as a mathematical expression.

The quotient of  and