Word Problems in Algebra - GED Math

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."

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."

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

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

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

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.

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.

After John has ate 2 candies out of his total of 48 candies, he has 46 candies left.

25% of 46 is equivalent to:

However, candies are counted in units, which means if John could have only given 11 candies to charity if he said he has given almost 25% away. The trick answer is 34 because 11.5 candies cannot be rounded to 12 candies.

Hence:

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.

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".

Every word problem has an unknown number. In this problem, the unknown number or value is the price of the shirt. The variable will represent the unknown number.

In this problem, will represent how much Mary spent for the shirt. The problem states that $48 was $14 less than 2 times what she spent on for the shirt. An equation will be written in order to solve this problem.

Then solve for .

The first step is to remove the subtraction of $14 by using the inverse operation, which would be addition. Remember, because it is an equation, whatever operation you choose to perform on one side of the equation must also be done to the other side of the equation. Therefore, you will add $14 to both sides of this equation.

In order to solve for , you will need to divide both sides by the coefficient, (the number next to the variable), which is 2.

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.

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:

Since Leslie has twice as many dimes as nickels, the number of nickels she has is half the number of dimes, or half of . This means she has nickels. Also, since she has four more quarters than dimes, she has quarters.

She has

in nickels,

in dimes, and

in quarters.

In total, the number of dollars Leslie has is

Leslie has dollars.

The number of pounds of coffee beans totals 50, so one of the equations would be

.

The total price of the Kona beans is the unit price, $24 per pound, multiplied by the quantity, pounds. This is dollars. Similarly, the total price of the Ethiopian delight beans is dollars, and the price of the mixture is dollars. Add the prices of the Kona and Ethiopian Delight beans to get the price of the mixture:

These are the equations of the system.

Let be the number of pizzas made and sold. Each pizza will require $2 worth of ingredients, so the ingredients in total will cost . Add this to the cost to rent the equipment and the cost will be .

The pizzas will cost $4.50 each, so the money raised will be .

The profit will be the difference between the revenue and the cost:

The French club wants a profit of at least $500, so we set up and solve the inequality:

At least 300 pizzas must be made and sold.

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,

To solve this equation, first get everything into the same units. Recall that there are ml for every one liter. Thus, liters are equal to ml. Now, what you basically have is a rate equation. Recall that the total work is represented as follows:

For your data, the total "work" is the ml. Start by calculating the time as a decimal:

This gives you:

However, remember that this is in seconds. You need to convert back to hours. You do this by dividing by , giving you . Rounding up, this gives you hours.

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.