Word Problems with One Unknown - Pre-Algebra
Card 1 of 200
You go to the store and buy apples. The apples cost $0.14 each. The cashier rings up your apples and says your total is $1.12 . How many apples did you buy?
You go to the store and buy apples. The apples cost $0.14 each. The cashier rings up your apples and says your total is $1.12 . How many apples did you buy?
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To solve, we will create an equation. We don't know how many apples we bought. When we don't know the value of something, we assign it a variable. so, the number of apples we bought will be x. Now, we know each apple cost $0.14. We can write this as
We also know that the total cost of the apples equals $1.12. We can write this as
Now, to solve for x we divide both sides by 0.14. We get
Therefore, we bought 8 apples.
To solve, we will create an equation. We don't know how many apples we bought. When we don't know the value of something, we assign it a variable. so, the number of apples we bought will be x. Now, we know each apple cost $0.14. We can write this as
We also know that the total cost of the apples equals $1.12. We can write this as
Now, to solve for x we divide both sides by 0.14. We get
Therefore, we bought 8 apples.
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A father is buying cheeseburgers for his children. Each cheeseburger costs $3.50. He spends $17.50 on cheeseburgers. How many cheeseburgers did he buy?
A father is buying cheeseburgers for his children. Each cheeseburger costs $3.50. He spends $17.50 on cheeseburgers. How many cheeseburgers did he buy?
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Set up and equation where 
is equal to the number of cheeseburgers:
Solve for c:
Set up and equation where
Solve for c:
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Grace is 4 years older than Elena. If Grace is 9 years old, how old is Elena?
Grace is 4 years older than Elena. If Grace is 9 years old, how old is Elena?
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Let Elena's be equal to 
:
Let Elena's be equal to
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The area of a square is 
. Find the length of one of its sides.
The area of a square is
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In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.
The area of a square is found using the following formula: 
.
Take the square root of each side.
In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.
The area of a square is found using the following formula:
Take the square root of each side.
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The area of a circle is 
. Find its radius.
The area of a circle is
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In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.
The area of a circle is found using the following formula: 
.
Divide each side by pi 
.
Take the square root of each side.
In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.
The area of a circle is found using the following formula:
Divide each side by pi
Take the square root of each side.
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The volume of a cube is 
. Find the length of one of its sides.
The volume of a cube is
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In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.
The volume of a cube is found using the following formula: 
.
Take the cube root of each side. The cube root is the number that is multiplied by itself three times in order to equal the original number.
In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.
The volume of a cube is found using the following formula:
Take the cube root of each side. The cube root is the number that is multiplied by itself three times in order to equal the original number.
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The volume of a cube is 
. Find the length of one of its sides.
The volume of a cube is
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In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.
The volume of a cube is found using the following formula: 
.
Take the cube root of each side. The cube root is the number that is multiplied by itself three times in order to equal the original number.
In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.
The volume of a cube is found using the following formula:
Take the cube root of each side. The cube root is the number that is multiplied by itself three times in order to equal the original number.
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An ice cream cone costs 
plus 
sales tax. How many ice cream cones can be purchased for 
?
An ice cream cone costs
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Calculate the cost of an ice cream cone with tax:
Determine how many cones, 
, can be purchased for 
by setting up the following equation:
Divide both sides by 3.18:
Therefore, 
ice cream cones can be purchased for 
.
Calculate the cost of an ice cream cone with tax:
Determine how many cones,
Divide both sides by 3.18:
Therefore,
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Suzie needs to ride her bike to the grocery store, which is is 15 miles away. It takes Suzie 45 minutes to bike to the grocery store. What is Suzies average speed? Express answer in miles per hour.
Suzie needs to ride her bike to the grocery store, which is is 15 miles away. It takes Suzie 45 minutes to bike to the grocery store. What is Suzies average speed? Express answer in miles per hour.
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Distance is the product of rate and time:
Plug in the information given in the problem, remembering that the questions says to state the answer in terms of miles per hour, and we are give her time in minutes. Change minutes to hours:
It took Suzie .75 hours to ride to the grocery store.
Suzie's rate is 
.
Distance is the product of rate and time:
Plug in the information given in the problem, remembering that the questions says to state the answer in terms of miles per hour, and we are give her time in minutes. Change minutes to hours:
It took Suzie .75 hours to ride to the grocery store.
Suzie's rate is
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Mary is 4 times as old as Juan. If Juan is 2 years old, how old is Mary?
Mary is 4 times as old as Juan. If Juan is 2 years old, how old is Mary?
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Write out an equation for the problem: 
where 
represents Juan's age and 
represents Mary's age.
Plug in Juan's age: 
Once we multiply, we find that Mary is 8 years old.
Write out an equation for the problem:
where
Plug in Juan's age:
Once we multiply, we find that Mary is 8 years old.
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Katie is three times as old as Ashley. If Katie is 18 years old, how old is Ashley?
Katie is three times as old as Ashley. If Katie is 18 years old, how old is Ashley?
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Write an equation for the problem: 
where a represents Ashley's age and 
represents Katie's age.
We plug in Katie's age: 
In order to solve for Ashley's age we divide both sides by 3. This will give us Ashley's age: 
years old.
Write an equation for the problem:
where a represents Ashley's age and
We plug in Katie's age:
In order to solve for Ashley's age we divide both sides by 3. This will give us Ashley's age:
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The ratio of students to teachers is 4 to 2. If there are 400 students, how many teachers are there?
The ratio of students to teachers is 4 to 2. If there are 400 students, how many teachers are there?
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We see that the ratio is 4 students to 2 teachers. Notice there are half as many teachers as there are students.
With this in mind, we can find the number of teachers by dividing the number of students by 2:
teachers.
We see that the ratio is 4 students to 2 teachers. Notice there are half as many teachers as there are students.
With this in mind, we can find the number of teachers by dividing the number of students by 2:
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If Jonathan saves $5.00 every week, how much would he have saved in 25 weeks?
If Jonathan saves $5.00 every week, how much would he have saved in 25 weeks?
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John makes $12.50/hour gardening. He earned $275 this week. Write the equation for figuring out his wages, and then solve it to find out how many hours he worked.
John makes $12.50/hour gardening. He earned $275 this week. Write the equation for figuring out his wages, and then solve it to find out how many hours he worked.
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Step 1: In order to find out how many hours John works, you first need a formula for calculating his wages:
(hourly wage)(hours)= total wages
Step 2: substitute the known values (hourly wage, total wages)
Step 3: isolate the unknown variable (hours) by dividing both sides by his hourly wage, then solve
Step 1: In order to find out how many hours John works, you first need a formula for calculating his wages:
(hourly wage)(hours)= total wages
Step 2: substitute the known values (hourly wage, total wages)
Step 3: isolate the unknown variable (hours) by dividing both sides by his hourly wage, then solve
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If 4 plums cost $5.50, then how much do 6 plums cost?
If 4 plums cost $5.50, then how much do 6 plums cost?
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In this proportions problem, you can solve for the cost of each plum in the first case. The problem says 4 plums cost $5.50, so
We can now use the value of x, or the cost of each plum, to calculate the cost of 6 plums.
.
The cost of 6 plums is $8.25.
In this proportions problem, you can solve for the cost of each plum in the first case. The problem says 4 plums cost $5.50, so
We can now use the value of x, or the cost of each plum, to calculate the cost of 6 plums.
The cost of 6 plums is $8.25.
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Jack needs to raise $200 for his trip. He plans to sell cookies for $0.25 per cookie. How many cookies would he need to sell to meet his goal?
Jack needs to raise $200 for his trip. He plans to sell cookies for $0.25 per cookie. How many cookies would he need to sell to meet his goal?
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Explanation:
Step 1: In order to find out how many cookies Jack needs to sell, you first need a formula.
(price/cookie)(number of cookies) = money needed
Step 2: Substitute the known values (price/cookie, money needed)
Step 3: Isolate the unknown variable (number cookies) by dividing both sides by (price/cookie), then solve:
Explanation:
Step 1: In order to find out how many cookies Jack needs to sell, you first need a formula.
(price/cookie)(number of cookies) = money needed
Step 2: Substitute the known values (price/cookie, money needed)
Step 3: Isolate the unknown variable (number cookies) by dividing both sides by (price/cookie), then solve:
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Choose the equation that will solve Amanda's scenario.
Amanda has 
bracelets she made that she plans to share with her friends. She wants to keep 
to give to her cousins. How many bracelets can she give to her friends?
Choose the equation that will solve Amanda's scenario.
Amanda has
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is the correct answer to this question.
Amanda originally has 
bracelets, so this is the number with which we begin.
Amanda is losing bracelets, so it is a subtraction problem.
Since the number we are solving for is the number of bracelets Amanda can give away, 
is placed after the subtraction sign.
The number of bracelets that Amanda needs to finish with is 
, so the equation is set to equal 
.
Amanda originally has
Amanda is losing bracelets, so it is a subtraction problem.
Since the number we are solving for is the number of bracelets Amanda can give away,
The number of bracelets that Amanda needs to finish with is
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Create an equation to solve the scenario.
Alex is the star player on his basketball team. For every basket he makes, his team receives 
points. Alex scored 
points in a game. How many baskets did he make?
Create an equation to solve the scenario.
Alex is the star player on his basketball team. For every basket he makes, his team receives
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The correct answer to the question is 
The number of points that Alex scored is 
, so set the equation equal to 
.
The unknown number that we are looking for is the number of baskets, so set 
equal to this.
Since each basket is worth 
points, multiply 
by 
.
The final equation comes out to be 
The correct answer to the question is
The number of points that Alex scored is
The unknown number that we are looking for is the number of baskets, so set
Since each basket is worth
The final equation comes out to be
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Create an equation to solve the scenario.
Megan needs 
dollars to buy a new pair of jeans. She received 
dollars from her grandmother for her birthday. Megan needs to figure out how much more she needs to save before she can buy the jeans.
Create an equation to solve the scenario.
Megan needs
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is the correct answer to this question.
Megan originally has 
dollars, so this is the number we begin with.
Megan needs to gain money, so this is an addition problem.
Since the number we are solving for is the amount of money that Megan needs to save, 
is placed after the addition sign.
The amount of money that Megan needs to save is 
dollars, so this is the number we set the equation equal to.
Megan originally has
Megan needs to gain money, so this is an addition problem.
Since the number we are solving for is the amount of money that Megan needs to save,
The amount of money that Megan needs to save is
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Create an equation for the scenario.
Lauren has 
dollars. She wants to buy necklaces that cost 
dollars each. How many necklaces is she able to buy?
Create an equation for the scenario.
Lauren has
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is the correct answer to this question.
The amount of money that Lauren has is 
dollars, so set the equation equal to 
.
On the opposite side of the equation, we solve for the unknown.
The unknown number that we are looking for is the number of necklaces she can buy, so set 
equal to this.
Since each necklace costs 
dollars, multiply 
by 
.
The amount of money that Lauren has is
On the opposite side of the equation, we solve for the unknown.
The unknown number that we are looking for is the number of necklaces she can buy, so set
Since each necklace costs
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