Word Problems Involving Linear Equations in One Variable

Word Problems Involving Linear Equations in One Variable

A REVIEW

Multiple Choice

The sum of three consecutive integers is 39. Which of the following representations could be used to solve the problem?

• 1st number - x

  2nd number - x + 1

  3rd number x + 2

• 1st number - x

  2nd number - x + 2

  3rd number x + 4

• 1st number - x

  2nd number - x + 2

  3rd number x + 3

Multiple Choice

The sum of three consecutive integers is 39. Which of the following equations could be used to solve the problem?

• x+x+2+x+3=39

• x+x+2+x+4=39

• x+x+1+x+2=39

Multiple Choice

The sum of three consecutive integers is 39. What are the numbers?

• 1st number - 12

  2nd number - 13

  3rd number - 14

• 1st number - 11

  2nd number - 12

  3rd number - 13

• 1st number - 11

  2nd number - 13

  3rd number - 15

Number Related Problem

x + x + 1 + x + 2 = 39
3x + 3 = 39
3x + 3 - 3 = 39 - 3
3x = 36

 $\frac{3x}{3}=\ \frac{36}{3}$  
x = 12 

Multiple Choice

Arn is three times Sheen's age. In ten years, Arn will be twelve years older than Sheen. Which representations would illustrate their present ages?

• Arn - 3x

  Sheen - x

• Arn - 3x + 10

  Sheen - x + 10

Multiple Choice

Arn is three times Sheen's age. In ten years, Arn will be twelve years older than Sheen. Which representations would illustrate their age 10 years from now?

• Arn - 3x

  Sheen - x

• Arn - 3x + 10

  Sheen - x + 10

Multiple Choice

Arn is three times Sheen's age. In ten years, Arn will be twelve years older than Sheen. Which of the following equations will be used to solve the problem?

• 3x + 10 = (x + 10) + 12

• 3x + 10 = (x + 10) - 12

Multiple Choice

Arn is three times Sheen's age. In ten years, Arn will be twelve years older than Sheen. What are their present ages?

• Arn is 18 years old and Sheen is 6 years old

• Arn is 6 years old and Sheen is 18years old.

• Arn is 28 years old and Sheen is 16 years old

Age Related Problem

3x + 10 = (x + 10) + 12
3x + 10 = x + 22
3x + 10 - 10 = x + 22 - 10
3x = x + 12
3x - x = x - x + 12
2x = 12

 $\frac{2x}{2}=\frac{12}{2}$  
x = 6 

Multiple Choice

Shane purposely broke her piggy bank because she wanted to donate goods to the fire victims in Inayawan, Cebu. She found out that she has a total of 140 bills consisting of Php 50.00 and Php 20.00 bills. The number of her 50 – peso bills is 10 less than four times the number of her 20 – peso bills. The total money she has is Php 6100.00. Which representations illustrate the number of bills?

• Php 50 ---- 4x - 10

  Php 20 ---- x

• Php 20 ---- 4x - 10

  Php 50 ---- x

• Php 50 ---- 4x + 10

  Php 20 ---- x

Multiple Choice

Shane purposely broke her piggy bank because she wanted to donate goods to the fire victims in Inayawan, Cebu. She found out that she has a total of 140 bills consisting of Php 50.00 and Php 20.00 bills. The number of her 50 – peso bills is 10 less than four times the number of her 20 – peso bills. The total money she has is Php 6100.00. Which representations illustrate the total value?

• 50(4x - 10)

  20x

• 20(4x - 10)

  50x

• 50(4x+10)

  20x

Multiple Choice

Shane purposely broke her piggy bank because she wanted to donate goods to the fire victims in Inayawan, Cebu. She found out that she has a total of 140 bills consisting of Php 50.00 and Php 20.00 bills. The number of her 50 – peso bills is 10 less than four times the number of her 20 – peso bills. The total money she has is Php 6100.00. Which equation illustrates the problem?

• 50(4x - 10) + 20x = 6100

• 20(4x - 10) + 50x = 6100

• 50(4x+10)+ 20x = 6100

Multiple Choice

Shane purposely broke her piggy bank because she wanted to donate goods to the fire victims in Inayawan, Cebu. She found out that she has a total of 140 bills consisting of Php 50.00 and Php 20.00 bills. The number of her 50 – peso bills is 10 less than four times the number of her 20 – peso bills. The total money she has is Php 6100.00. How many 50 – peso and 20 – peso bills does she have?

• There are 30 pcs of 20-peso bills and 110 pcs of 50 - peso bills.

• There are 110 pcs of 20-peso bills and 30 pcs of 50 - peso bills.

Money Related Problem

50(4x - 10) + 20x = 6100
200x - 500 + 20x = 6100
220x - 500 = 6100
220x - 500 + 500 = 6100 + 500
220x = 6600

 $\frac{220x}{220}=\ \frac{6600}{220}$  
x = 30 

Php 20 (30 pcs)
Php 50 (110 pcs)

Multiple Choice

Jean takes 10 hours to prepare the tickets for the Kindred Hearts. Sharina helps her and together they finish the job in 5 hours. Which expression represents the rate of Sharina?

•  $\frac{1}{x}$  

•  $\frac{5}{x}$   

•  $\frac{1}{5}$  

•  $\frac{1}{2}$  

Multiple Choice

Jean takes 10 hours to prepare the tickets for the Kindred Hearts. Sharina helps her and together they finish the job in 5 hours. Which equation represents the problem?

•  $\frac{1}{2}+\ \frac{5}{x}=1$  

•  $\frac{x}{2}+\frac{5}{x}=\ 1$   

Multiple Choice

Jean takes 10 hours to prepare the tickets for the Kindred Hearts. Sharina helps her and together they finish the job in 5 hours. How long will it take Sharina to finish the task alone?

• 5 hours

• 10 hours

• 2 hours

Work Related Problem

 $\frac{1}{2}+\frac{5}{x}=\ 1$  
 $\left(2x\right)\left(\frac{1}{2}+\frac{5}{x}\right)\ =\ 1\left(2x\right)$  
 $\frac{2x}{2}+\frac{10x}{x}=\ 2x$  
x + 10 = 2x 
2x = x + 10 
2x - x = x - x + 10
x = 10