# GED Math : Word Problems in Algebra

## Example Questions

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### Example Question #1 : Word Problems In Algebra

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

The opposite of the difference of a number and twenty-four

Twenty-four decreased by the absolute value of a number

Twenty-four decreased by the opposite of a number

The absolute value of a number decreased by twenty-four

Twenty-four decreased by the absolute value of a number

Explanation:

is twenty-four decreased by , which is the absolute value of a number, so  is "twenty-four decreased by the absolute value of a number."

### Example Question #2 : Word Problems In Algebra

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

The opposite of the difference of a number and fifty-four

The absolute value of the product of a number and negative fifty-four

The absolute value of the difference of a number and fifty-four

The opposite of the product of a number and negative fifty-four

The absolute value of the difference of a number and fifty-four

Explanation:

is the absolute value of , which is the difference of a number and fifty-four; therefore,  is "the absolute value of the difference of a number and fifty-four."

### Example Question #3 : Word Problems In Algebra

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

Three decreased by the square of a number

The square of the difference of three and a number

The square of the difference of a number and three

The square of a number decreased by three

Three decreased by the square of a number

Explanation:

is three decreased by , which is the square of a number; therefore,  is three decreased by the square of a number.

### Example Question #4 : Word Problems In Algebra

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

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

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 opposite of the difference of a number and forty-five

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.

### Example Question #5 : Word Problems In Algebra

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

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

Sixty-five subtracted from the absolute value of a number

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

Sixty-five subtracted from the opposite of a number

Sixty-five subtracted from the opposite of a number

Explanation:

is sixty-five subtracted from , which is the opposite of a number; therefore,  is "sixty-five subtracted from the opposite of a number."

### Example Question #6 : Word Problems In Algebra

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

The square of the difference of thirty-four and a number

Twice the difference of a number and thirty-four

The square of the difference of a number and thirty-four

Twice the difference of thirty-four and a number

The square of the difference of a number and thirty-four

Explanation:

is the square of , which is the difference of a number and thirty-four. Therefore,  is the difference of a number and thirty-four.

### Example Question #7 : Word Problems In Algebra

A broken television cost $1.25 after a 99% discount. What was the original price? Possible Answers:$12.50

$125$2.74

$2.49$250

$125 Explanation: Let x be the original price. If the original price was given a discount, the value of the percent discount must be subtracted from the original price. ### Example Question #8 : Word Problems In Algebra Which of the following phrases can be represented by the algebraic expression ? Possible Answers: Five decreased by the reciprocal of a number Five less than by the reciprocal of a number The reciprocal of the difference of a number and five The reciprocal of the difference of five and a number Correct answer: The reciprocal of the difference of five and 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". ### Example Question #9 : Word Problems In Algebra Sixty-four coins, all dimes and nickels, total$5.15. How many of the coins are dimes?

Explanation:

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

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

, the number of dimes.

### Example Question #10 : Word Problems In Algebra

Above is the menu for a coffee shop; there is no sales tax charged on purchases.

Greg is throwing a party and wants to buy eight large cappucinos, one for each attendee. He wants to buy all the butter croissants he can without spending more than \$80 total. How many croissants will he be able to buy?

Explanation:

Eight large cappucinos will cost Greg

.

This leaves him

to buy croissants, which cost .

Let  be the number of croissants he buys. Then

Greg can buy up to 21 croissants.

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