SOLVING LINEAR EQUATIONS IN ONE VARIABLE WORD PROBLEMS

Problem 1 :

A math teacher gives her class the following problem. Barry is selling magazine subscriptions for a school fundraiser.

He has already sold 15 subscriptions. He plans to sell 3 subscriptions per week until he reaches a total of 30 subscriptions sold. How many weeks will it take Barry to achieve his goal.

Solution :

Number of subscriptions that he already sold = 15

Number of subscriptions per week = 3

Let x be the number of weeks required to to reach 30 subscriptions.

15 + 3x = 30

3x = 30 - 15

3x = 15

x = 15/3

x = 5

So, to achieve his goal Barry will take 5 weeks.

Problem 2 :

A trampoline park costs $12 for the first hour and $6 for each additional hour.

Flynn pays $30 at the trampoline park. Write the equation that represents the given situation and find the number of additional hours Flynn stays at the trampoline park after the first hour.

Solution :

Cost for the first hour = $12

Cost for each additional hour = 6

Let x be the number of additional hours.

12 + 6x = 30

6x = 30 - 12

6x = 18

x = 18/6

x = 3

So, the number of additional hours is 3.

Problem 3 :

Tim's phone service charges $25.82 plus an additional $0.20 for each text message sent per month. If Tim's phone bill was $30.82, which equation could be used to find how many text messages, x, Tim sent last month?

Solution :

Number of text messages = x

Service charge = $25.82

Additional charge for each text message = 0.20

Total bill = 30.82

25.82 + 0.20x = 30.82

0.20x = 30.82 - 25.82

0.20x = 5

x = 5/0.20

x = 25

So, the number of text messages in the last month is 25.

Problem 4 :

Ryan is performing an experiment. He starts with a solution that has a temperature of 12.2°C. He lowers the temperature 5 times by the same amount each time. He stopped the experiment when the temperature of the solution was was -14.61°C.

Which equation can be used to find x, the number of degrees he lowered the temperature by each time?

Solution :

The initial temperature = 12.2

The amount of temperature lowers = x

12.2 - 5x = -14.61

12.2 + 14.61 = 5x

5x = 26.81

x = 26.81/5

x = 5.362

So, the every time number of degrees he lowered is 5.362°C

Problem 5 :

Ruth has 12 rolls at her bakery. She receives an online order for 60 rolls. Ruth bakes rolls in batches of 24. Write the equation that represents the given situation and find the number of batches Ruth needs to make to complete the order.

Solution :

Number of rolls in her bakery = 12

Number of online order = 60

Number of rolls can be made in each batch = 24

Number of batches required = x

12 + 24x = 60

24x = 60 - 12

24x = 48

x = 48/24

x = 2

So, two batches is required.

Problem 6 :

Mary spent a total of $291.63 for a party. She spent $200.67 on food, plus an additional $30.32 for each hour of the party. How long was the party?

Solution :

Let x be the number of additional hour.

Total amount spent = 291.63

Amount already spent for food = 200.67

Charge for each additional hour = 30.32

200.67 + 30.32 x = 291.63

30.32x = 291.63 - 200.67

30.32x = 90.96

x = 90.96/30.32

x = 3

So, number of additional hour she spent is 3.

Problem 7 :

An oil drilling company drills the same distance each day for 5 days. They started at an elevation of 121.175 feet and ended at an elevation of -246.875 feet. Which equation can be used to find x, the distance they drilled each day?

Solution :

Let x be the height drilled on each day

121.175 + 5x = -246.875

5x = -246.875 - 121.175

5x = -368.05

x = -368.05/5

x = -73.61

So, the length has been drilled on each day is 73.61

Problem 8 :

Tim and Tom are trying to earn money to buy a new game system over a 3-month period. Tim saved $45.88 each month. If they need a total of $213.33 to buy the game system, how much does Tom need to earn each of the 3 months in order to buy the game system?

Solution :

Amount he saves on each month = 45.88

Amount required for the same system = 213.33

Let x be the amount to be saved.

Number of months he is planning to work = 3

45.88 + 3x = 213.33

3x = 213.33 - 45.88

3x = 167.45

x = 167.45/3

x = 55.81

So, each month he has to save $55.81.