# GED Math : Single-Variable Algebra

## Example Questions

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### Example Question #161 : Algebra

After a  discount, a pair of shoes costs . What was the original price of the shoes?

Explanation:

Let  be the original price of the shoes. Since the shoes were  off, we can write the following equation:

Now, solve for .

The shoes originally cost .

### Example Question #30 : Word Problems In Algebra

Joseph is responsible for planning his company's holiday party. He has been given a budget of  for renting a venue and providing dinner for all the attendees. The cost for renting a venue is . He expects  employees to show up to the party. Which inequality shows how to find the amount, , that Joseph can spend on dinner for each person?

Explanation:

Since Joseph has a budget of , that means he cannot spend above that amount. This translates to the use of the less than or equal sign, , in the inequality.

The total cost for the dinner for all the attendees can be found by multiplying the number of attendees by the cost of each dinner, .

The rental of the venue is a one-time payment.

Thus, we can write the following inequality:

### Example Question #161 : Single Variable Algebra

A delivery service charges a  delivery flat fee then an additional  for each ounce the package weighs. Which of the following expressions would give the total cost for the delivery of an item weighing  ounces?

Explanation:

Since the company charges  per ounce, an item weighing  ounces would then cost  to ship, based on weight alone. The question also states that there is a flat  fee for each delivery.

Thus we can write the following expression to represent the total cost of shipping:

### Example Question #31 : Word Problems In Algebra

A sweater originally priced at  dollars goes on sale for  off. After a week, the sweater's price is further reduced , and then it was sold. Which of the following expressions would be the price of the price the sweater sold for?

Explanation:

Start by finding the price of the sweater after the first price cut. Since it was  off, we can write the following:

The sweater cost  after the first price cut.

Then, find the price when after the second price cut, which was  the already discounted price.

### Example Question #162 : Single Variable Algebra

An ambulance service charges  for the initial call, then  per mile it takes to get to the hospital. Which of the following expressions represents the cost of taking an ambulance  miles to the hospital?

Explanation:

Start by finding out how much it will take to take the ambulance  miles. Since it costs  per mile, then  represents the cost of just the travel. Next, you need to include the fixed cost of .

Thus, the total cost of the ambulance trip is expressed with .

### Example Question #163 : Single Variable Algebra

A number, when multiplied by  gives us a result of . Find the number.

Explanation:

Lets say that this number is . If we follow what the question is saying, we come up with the equation:

We will divide both sides by 4 to isolate  on the left side.

So,

We simplify:

### Example Question #164 : Single Variable Algebra

This winter, it snowed ten more inches than five times the amount of snow the previous winter, during which it snowed one half as much as the winter before that. If two years ago it snowed twenty inches, how much did it snow this winter?

Explanation:

For simplicity, let's call our years , and , with  being the amount of snow it snowed two years ago,  being the amount of snow it snowed last year, and  being the amount of snow it snowed this year. Now, we know that year  is .  Based on this, we can say that  is .  Finally, we know that year year  could be written:

Based on our data, this is:

### Example Question #31 : Word Problems In Algebra

Marge and William are running away from each other in opposite directions. Marge is running at a rate of , while William is running at a rate of .  In how many minutes will they be  from each other?

Explanation:

Every second, you know that Marge and William will become a total of  or .  Now, you can use the simple work formula for distance:

or, for our data,

(Remember  kilometers is  meters.)

Thus, solving for  you get:

This is in seconds, though. You need minutes. To convert, you need to divide by :

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