Pre-Algebra : Word Problems with One Unknown

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #21 : Word Problems

Mike and his 2 brothers decided to buy a new video game console. If Mike and his brothers each paid $49, how much did the video game console cost?

Possible Answers:

$137

$145

$147

$155

$98

Correct answer:

$147

Explanation:

To solve this simple word problem, we need to understand what it is saying. The problem tells us that Mike and his brothers (three people in all) paid $49 apiece for a video game console. This means we need to multiply what each person paid by the number of people:

\displaystyle \small Cost = 49*3

\displaystyle \small =147

The total cost of the video game console was $147.

Example Question #22 : Algebraic Equations

Choose the equation that will solve Amanda's scenario.

Amanda has \displaystyle 20 bracelets she made that she plans to share with her friends. She wants to keep \displaystyle 6 to give to her cousins. How many bracelets can she give to her friends?

Possible Answers:

\displaystyle 20 + x = 14

\displaystyle 14 - x = 6

\displaystyle 14 + 6 = x

\displaystyle 6 + x = 14

\displaystyle 20 - x = 6

Correct answer:

\displaystyle 20 - x = 6

Explanation:

\displaystyle 20 - x = 6 is the correct answer to this question.

Amanda originally has \displaystyle 20 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, \displaystyle x is placed after the subtraction sign.

The number of bracelets that Amanda needs to finish with is \displaystyle 6, so the equation is set to equal \displaystyle 6.

Example Question #23 : Algebraic Equations

Create an equation to solve the scenario.

Alex is the star player on his basketball team. For every basket he makes, his team receives \displaystyle 2 points. Alex scored \displaystyle 22 points in a game. How many baskets did he make?

Possible Answers:

\displaystyle 2x=22

\displaystyle x + 2 = 22

\displaystyle 22 - x = 20

\displaystyle x - 2 = 22

\displaystyle 22 - 20 = x

Correct answer:

\displaystyle 2x=22

Explanation:

The correct answer to the question is \displaystyle 2x=22

The number of points that Alex scored is \displaystyle 22, so set the equation equal to \displaystyle 22.

The unknown number that we are looking for is the number of baskets, so set \displaystyle x equal to this.

Since each basket is worth \displaystyle 2 points, multiply \displaystyle x by \displaystyle 2.

The final equation comes out to be \displaystyle 2x = 22

Example Question #24 : Algebraic Equations

Create an equation to solve the scenario.

Megan needs \displaystyle 50 dollars to buy a new pair of jeans. She received \displaystyle 35 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.

Possible Answers:

\displaystyle $35 + x = $50

\displaystyle $50 + $35 = x

\displaystyle $50x = $35

\displaystyle 2x = $50

\displaystyle $35x = $50

Correct answer:

\displaystyle $35 + x = $50

Explanation:

\displaystyle $35 + x = $50 is the correct answer to this question.

Megan originally has \displaystyle 35 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, \displaystyle x is placed after the addition sign.

The amount of money that Megan needs to save is \displaystyle 50 dollars, so this is the number we set the equation equal to.

Example Question #25 : Algebraic Equations

Create an equation for the scenario.

Lauren has \displaystyle 15 dollars. She wants to buy necklaces that cost \displaystyle 3 dollars each. How many necklaces is she able to buy?

Possible Answers:

\displaystyle $15 = $3x

\displaystyle $15x = $3

\displaystyle $15 + $3 = x

\displaystyle $15 - $3 = x

\displaystyle $3 - x = $15

Correct answer:

\displaystyle $15 = $3x

Explanation:

\displaystyle $15 = $3x is the correct answer to this question.

The amount of money that Lauren has is \displaystyle 15 dollars, so set the equation equal to \displaystyle 15.

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 \displaystyle x equal to this.

Since each necklace costs \displaystyle 3 dollars, multiply \displaystyle x by \displaystyle 3
 

Example Question #22 : Word Problems

Ian and his two friends bought a pizza. They divided the pizza into twelve slices. If divided evenly, how many slices can Ian eat? 

Possible Answers:

\displaystyle 2

\displaystyle 4

\displaystyle 6

\displaystyle 3

\displaystyle 12

Correct answer:

\displaystyle 4

Explanation:

The problem is asking you to divide 12 into three parts.

We divide 12 by 3. By factoring 12 we see that the 3's cancel and we are left with 4.

 \displaystyle \frac{12}{3}=\frac{4\cdot 3}{3}=4

Example Question #23 : Word Problems With One Unknown

Sally's Mom gave Sally \displaystyle \$20 to go buy cookies at the store. If each cookie costs \displaystyle \$2, how many cookies can Sally's \displaystyle \$20 buy? 

Possible Answers:

\displaystyle 20 \text{ cookies}

\displaystyle 5 \text{ cookies}

\displaystyle 15 \text{ cookies}

\displaystyle 10 \text{ cookies}

Correct answer:

\displaystyle 10 \text{ cookies}

Explanation:

The question is asking you to divide the $20 by the cost of one cookie.

In this problem each cookie costs $2. 

\displaystyle \frac{20}{2}= 10

Therefore, with $20 Sally can buy 10 cookies.

Example Question #22 : Word Problems

Matt was \displaystyle 7 years old in \displaystyle 2000. How old is Matt in \displaystyle 2007?

Possible Answers:

\displaystyle 17\text{ years old}

\displaystyle 14 \text{ years old}

\displaystyle 15 \text{ years old}

\displaystyle 9\text{ years old}

Correct answer:

\displaystyle 14 \text{ years old}

Explanation:

The question is asking you to add 7 years to Matt's age because \displaystyle 2007-2000=7.

Adding his age from 2000 to the number of years that have past from 2000 to 2007 we get his new age. 

\displaystyle 7 +7 =14

Example Question #23 : Word Problems

Adam bought \displaystyle 20 pieces of candy at lunch. By dinner, Adam only had \displaystyle 5 pieces left. How many pieces did Adam eat?

Possible Answers:

\displaystyle 15

\displaystyle 20

\displaystyle 5

\displaystyle 10

Correct answer:

\displaystyle 15

Explanation:

The question is asking you to subtract the 5 pieces leftover from the original amount of 20. 

\displaystyle 20-5=15

Example Question #23 : Word Problems

Joe is traveling by car and his average speed is \displaystyle 55 mph. If his destination is \displaystyle 385 mi away, how many hours will it take Joe to arrive if he travels his average speed?

Possible Answers:

\displaystyle 7 hrs

\displaystyle 5 hrs

\displaystyle 10 hrs

\displaystyle 55 hrs

\displaystyle 60 hrs

Correct answer:

\displaystyle 7 hrs

Explanation:

You are given two knowns; the rate of travel is \displaystyle 55 mph, and the distance Joe needs to travel is \displaystyle 385 mi. To find how long it takes Joe to get to his destination, we can set up a simple algebraic expression. Let \displaystyle x stand for our unknown travel time:

\displaystyle \left ( 55mph\right ) \times x hrs = 385 mi   

To solve for \displaystyle x, divide both sides by \displaystyle 55 mph

\displaystyle x = 7hrs

 

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