Word Problems in Algebra - GED Math
Card 1 of 180
Which of the following phrases can be written as the algebraic expression 
?
Which of the following phrases can be written as the algebraic expression
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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.
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Which of the following phrases can be written as the algebraic expression 
?
Which of the following phrases can be written as the algebraic expression
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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."
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Which of the following phrases can be written as the algebraic expression 
?
Which of the following phrases can be written as the algebraic expression
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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."
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Which of the following phrases can be written as the algebraic expression 
?
Which of the following phrases can be written as the algebraic expression
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is three decreased by 
, which is the square of a number; therefore, 
is three decreased by the square of a number.
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Which of the following phrases can be written as the algebraic expression 
?
Which of the following phrases can be written as the algebraic expression
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is sixty-five subtracted from 
, which is the opposite of a number; therefore, 
is "sixty-five subtracted from the opposite of a number."
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Which of the following phrases can be written as the algebraic expression 
?
Which of the following phrases can be written as the algebraic expression
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is the square of 
, which is the difference of a number and thirty-four. Therefore, 
is the difference of a number and thirty-four.
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A broken television cost $1.25 after a 99% discount. What was the original price?
A broken television cost $1.25 after a 99% discount. What was the original price?
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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.
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.
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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?
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?
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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.
Eight large cappucinos will cost Greg
This leaves him
to buy croissants, which cost
Let
Greg can buy up to 21 croissants.
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John had 48 candies. He ate 2, and said he gave almost 25% of the remaining to charity. What is the most reasonable number of candies he had left?
John had 48 candies. He ate 2, and said he gave almost 25% of the remaining to charity. What is the most reasonable number of candies he had left?
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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:
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:
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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?
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?
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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.
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.
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Which of the following phrases can be represented by the algebraic expression 
?
Which of the following phrases can be represented by the algebraic expression
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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".
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Mary spent $48 for shoes. This was $14 less than twice what she spent for a shirt. How much was the shirt?
Mary spent $48 for shoes. This was $14 less than twice what she spent for a shirt. How much was the shirt?
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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.
Every word problem has an unknown number. In this problem, the unknown number or value is the price of the shirt. The variable
In 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
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Sixty-four coins, all dimes and nickels, total $5.15. How many of the coins are dimes?
Sixty-four coins, all dimes and nickels, total $5.15. How many of the coins are dimes?
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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
An equation can be set up and solved for
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Sixty-four coins, all dimes and quarters, total $8.95. How many quarters are there?
Sixty-four coins, all dimes and quarters, total $8.95. How many quarters are there?
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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:
Let
An equation can be set up and solved for
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Leslie has some nickels, some dimes, and some quarters. She has twice as many dimes as she has nickels, and she has four more quarters than she has dimes. If she has 
dimes, how much does she have, in terms of 
, in nickels, dimes, and quarters?
Leslie has some nickels, some dimes, and some quarters. She has twice as many dimes as she has nickels, and she has four more quarters than she has dimes. If she has
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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.
Since Leslie has twice as many dimes as nickels, the number of nickels she has is half the number of dimes, or half of
She has
In total, the number of dollars Leslie has is
Leslie has
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Jeff, the barista at Moonbucks Coffee, is having a problem. He needs to make fifty pounds of Premium Blend coffee by mixing together some Kona beans, which cost $24 per pound, with some Ethiopian Delight beans, which cost $10 per pound. The Premium Blend coffee will cost $14.20 per pound. Also, the coffee will sell for the same price mixed as it would separately.
Let 
be the number of pounds of Kona beans and 
be the number of pounds of Ethiopian Delight beans. Which of the following systems of equations could you set up to solve this problem?
Jeff, the barista at Moonbucks Coffee, is having a problem. He needs to make fifty pounds of Premium Blend coffee by mixing together some Kona beans, which cost $24 per pound, with some Ethiopian Delight beans, which cost $10 per pound. The Premium Blend coffee will cost $14.20 per pound. Also, the coffee will sell for the same price mixed as it would separately.
Let
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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.
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,
These are the equations of the system.
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The French club wants to make and sell some pizzas for a fundraiser. It will cost $250 to rent the equipment to make the pizzas and $2 worth of ingredients to make each pizza. The pizzas will be sold for $4.50 apiece.
How many pizzas must be made and sold for the French club to make a profit of at least $500?
The French club wants to make and sell some pizzas for a fundraiser. It will cost $250 to rent the equipment to make the pizzas and $2 worth of ingredients to make each pizza. The pizzas will be sold for $4.50 apiece.
How many pizzas must be made and sold for the French club to make a profit of at least $500?
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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.
Let
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.
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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.)
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
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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, 
This kind of question is really just a basic rate problem. What it is asking is "How many months
Thus, you can set up the equation:
Thus,
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A tank leaks at a rate of 
ml per second. How many hours will it take for the tank to drain, given that it is 
liters? Round to the nearest hour.
A tank leaks at a rate of
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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.
To solve this equation, first get everything into the same units. Recall that there are
For your data, the total "work" is the
This gives you:
However, remember that this is in seconds. You need to convert back to hours. You do this by dividing by
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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?
A writer make
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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.
This question could be set up like an equation as follows:
The variable
Now, don't be tricked! You can't sell partial books. Thus, you will need to sell
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