Word Problems in Algebra

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GED Math › Word Problems in Algebra

Questions 1 - 10
1

Timmy works at a fast food chain retail store five days a week, eight hours a day. Suppose it costs him $2.00 everyday to drive to and from work. He makes $10.00 per hour. How much will Timmy have at the end of the week, before applicable taxes?

Explanation

Timmy makes ten dollars per hour for eight hours.

For five days:

Timmy also will pay for the week to get to work and back.

Subtract his expense from his earnings for the week.

Timmy will have by the end of the week.

2

The fare for a taxi meter is calculated as follows: Each fare will have an initial charge to pick someone up. Then, is added for each mile driven. Which of the following expressions illustrates the taxi fare if an individual took a trip miles long?

Explanation

First, calculate the cost for the miles driven. Since the rider will be charged for every mile driven, we can write the expression to illustrate the total mileage cost.

Next, since the problem states that will be a one-time charge on the fare, we can then write the following expression to illustrate the total cost of a taxi ride of miles:

3

Ten less than three times a number squared is 182. What is the number?

Explanation

Translate the words into a mathematical equation. "Three times a number squared" can be written as . "Less " is telling you to subtract from .

We can then write the following equation, then solve for .

4

Which of the following phrases can be written as the algebraic expression ?

The opposite of the difference of a number and forty-five

The absolute value of the difference of a number and forty-five

The opposite of the difference of forty-five and a number

The absolute value of the difference of forty-five and a number

Explanation

is the opposite of , which is the difference of a number and forty-five; therefore, is the opposite of the difference of a number and forty-five.

5

Which of the following phrases can be represented by the algebraic expression ?

The reciprocal of the difference of five and a number

The reciprocal of the difference of a number and five

Five decreased by the reciprocal of a number

Five less than by the reciprocal of a number

Explanation

is the reciprocal of , which is the difference of five and a number. Therefore, is "the reciprocal of the difference of five and a number".

6

Sixty-four coins, all dimes and quarters, total $8.95. How many quarters are there?

Explanation

Let be the number of quarters. Then there are dimes.

An equation can be set up and solved for for the amount of money in dollars:

7

A writer make dollars of profit per book sold. The printing run of a lot of books cost dollars. How many books must the author sell before the book becomes profitable?

Explanation

This question could be set up like an equation as follows:

The variable indicates the number of books that would have to be sold. This comes out to:

Now, don't be tricked! You can't sell partial books. Thus, you will need to sell books in order to turn a profit. If you only sell , you will not have sold enough to make a profit.

8

Suppose a customer paid $500 for a new phone. The store had applied a 20% discount, and the tax after the discount was 8.25%. What was the approximate price of the phone before the applied discount and tax rate?

$577.37

$573.37

$580.37

$583.37

$592.37

Explanation

Let x be the cost of the phone before applying the 20% discount. After applying the discount, the value will be equal to some amount y before applying tax.

After amount y has been taxed the 8.25%, the new value will be the price of the phone, which is $500. The equation representing this relationship is:

We have a system of equations. Substitute y in terms of x into the 2nd equation. Solving the value of x will give the original value of the phone.

Therefore, the price of the phone is approximately $577.37.

9

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 .

10

Pat makes fifteen birdhouses every month, while John makes twenty. If the two men work together to make birdhouses, how long will it take them to make of them? (Presume that they make the houses separately and do not interfere with each other's work.)

months

months

months

months

Cannot be computed from the data given

Explanation

This kind of question is really just a basic rate problem. What it is asking is "How many months at rate does it take to make birdhouses?" The rate is just the combination of the two men's rates:

Thus, you can set up the equation:

Thus,

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