Pre-Algebra : Word Problems with One Unknown

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #41 : Word Problems With One Unknown

A bus has eleven children on it at the beginning of its route.  Fourteen get on at the first stop, and twelve get on at the stop after that.  How many children are on the bust after the third stop?

Possible Answers:

Correct answer:

Explanation:

To solve a word problem with an unknown quantity, treat the unknown quantity as a variable.  The best equation for the problem above is:  

 

then solve:

 

Example Question #42 : Word Problems

To pass the exam, Frannie needs to score at least twelve of the fourteen possible points.  However, she only scored nine points.  How many points short was she of passing?

Possible Answers:

Correct answer:

Explanation:

To solve a word problem with an unknown quantity, treat the unknown quantity as a variable.  The best equation for the problem above is:  

 

then solve

 

 

Example Question #41 : Word Problems With One Unknown

If Johnny had  apples yesterday, and only  today, how many apples did Johnny lost overnight?

Possible Answers:

Correct answer:

Explanation:

To solve a word problem with an unknown quantity, treat the unknown quantity as a variable.  The best equation for the problem above is:

use algebra to solve

Example Question #43 : Word Problems

Paula was given  dollars by her mother to do her grocery shopping.  Everything she bought came to a total of .  How much money does she have left over?  Round your answer to the nearest cent.

Possible Answers:

Correct answer:

Explanation:

To solve a word problem with an unknown quantity, treat the unknown quantity as a variable.  The best equation for the problem above is:  

 

use algebra to solve

Example Question #41 : Word Problems

Jon is 5 years older than twice Vicki's age. Vicki is 21 years old. How old is Jon?

Possible Answers:

Jon is 26 years old.

Jon is 47 years old.

Jon is 48 years old.

Jon is 68 years old.

Jon is 37 years old.

Correct answer:

Jon is 47 years old.

Explanation:

In this problem we have one unknown, Jon's age. 

We must list what we do know:

Vicki is 21 years old.

Jon is twice Vicki's age plus 5 years

If we let J=Jon's age we could setup an easy equation:

so Jon is twice Vicki's age, 21, plus 5 more years. If we solve the equation we find out that Jon is 47 years old:

Example Question #42 : Algebraic Equations

You go to the store and buy groceries. Your total is $24.63. The cashier gives you $10.37 in change. How much did you give the cashier?

Possible Answers:

Correct answer:

Explanation:

We can solve this problem by setting up a simple equation.  We do not know the amount we paid, so we will assign that a variable, x.  So, 

We know that if we subtract the total from the amount we pay, we will get the amount of change.  So, we will solve for x.  We must add $24.63 to both sides.  We get

Therefore, we gave the cashier $35.

 

Example Question #47 : Word Problems

Michael plays basketball and makes  more free throws than twice what Eli makes.

Together they make  free throws.

How many does Eli make?

Possible Answers:

Correct answer:

Explanation:

Michael makes  more than twice Eli. 

If Eli makes  then double that and add  and that would be Michael's amount.

Eli makes  free throws.

Example Question #44 : Word Problems

Write the equation for the word problem then solve.

Jacob spent $60 on a birthday cake. This is $30 more than he spent for his brother's birthday gift. How much did he spend on his brother's birthday gift? Please include the equation in your answer.

Possible Answers:

Correct answer:

Explanation:

In this problem there is one unknown and in this case it is how much Jacob spent on his brother's birthday gift. 

Let x=the amount of money spent on his birthday gift. We know that he spent $30 more on the birthday cake than on his brother's gift, so  because he spent $60 on the birthday cake.

Solving for the equation we have:

Example Question #43 : Word Problems

You go to the store and buy 9 bottles of water.  You spend $11.25 for all.  How much is each bottle of water?

Possible Answers:

Correct answer:

Explanation:

When you do not know the value of something, you assign it a variable.  In this case, we do not know how much a bottle of water costs, so we will assign it a variable.  We know we bought 9 bottles.  We also know that our total cost is $11.25.  So, we can set up the equation.  We get

where x is the cost of a bottle of water.  Now, we solve for x.  We must divide both sides by 9.  We get

Therefore, a bottle of water costs $1.25.

Example Question #42 : Word Problems

Sarah is building a fence for her dog's square play area. To reduce the cost, she is using her house as 1 side of the play area, meaning she only has to purchase fencing for the other sides. If she needs to fence in 225 meters2 for her dogs, and fencing costs $2.50 per meter of fencing, what will be the cost of fencing in this square play area?

Possible Answers:

Correct answer:

Explanation:

The first step is to figure out the perimeter of the square play yard with an area of 225 meters, first using the fomula: 



Find the square root of both sides to calculate the length of the base of the square



All the sides are of equivilent length, so the total amount of fence required is:



One side is "fenced" by the house, so that fenching does not need to be paid for. Thus, only the remaining 3 sides need to be paid for.

Finally, multiply the length of fencing needs by the cost of fence per foot to find your answer: 




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