ALGEBRA WORD PROBLEMS ON LINEAR EQUATIONS IN ONE VARIABLE

Problem 1 :

It took Thomas 25 minutes longer to do his math homework than to do his French homework. He spent a total of 2.25 hours on both subjects. How much time did he spend on math?

Solution :

Let x be the time taken to complete his French homework.

Time taken to complete math homework = (x + 25) minutes

Total time spent for both subjects = 2.25 hours

1 hour = 60 minutes

2.25 hours = 2.25 (60)

= 135 minutes

x + x + 25 = 135

2x + 25 = 135

2x = 135 - 25

2x = 110

x = 110/2

x = 55 minutes

Problem 2 :

Jesse earns $6 an hour babysitting for his younger brother. His mom gave him $71 last week. This included his babysitting money and his $20 allowance. How many hours did Jesse babysit?

Solution :

Number of hours she is taking for baby sitting = x

Amount she receives for one hour of babysitting = 6

Her allowance = 20

6x + 20 = 71

6x = 71 - 20

6x = 51

x = 51/6

x = 17/2

x = 8.5

So, she is receiving $8.5 for one hour of babysitting. 

Problem 3 :

Carol and Cathy are each saving money for a vacation. Carol started with $25 and saves $7.50 a week. Cathy started with $10 and saves $10 a week. When will they have saved the same amount?

Solution :

Let x be the number of weeks that they are saving.

Amount saved by Carol  = 25 + 7.50 x

Amount saved by Cathy = 10 + 10x

They are saving the same amount, then 

25 + 7.50x = 10 + 10x

25 - 10 = 10x - 7.50x

15 = 2.50x

x = 15/2.50

x = 6

So, at the end of the 6th week they will have the same amount.

Problem 4 :

One weekend Bill earned 3 times as much as Jim. Tom earned $5 more than Jim. In all, they earned $60. How much did each earn?

Solution :

Let x be the amount Jim is earning.

Amount earned by Tim = 5 + x

Amount earned by Bill = 3x

They added together = 60

x + 5 + x + 3x = 60

5x + 5 = 60

5x = 60 - 5

5x = 55

x = 55/5

x = 11

Problem 5 :

The Maxwell children have hired a caterer to provide food for an anniversary party for their parents. The caterer has quoted a price of $96 per person and is asking for an advance payment of one-fourth of the total bill. If the advance payment is $1200, how many guests are invited to the party?

Solution :

Advance payment = 1200

Advance payment = 1/4 of total bill

Let x be the total bill

1200 = (1/4) x 

1200 = x/4

x = 1200(4)

x = 4800

Price per person = $96

Let n be the number of guests.

Product of number of guests and cost spent for each person

96 n = 4800

x = 4800/96

x = 50

So, number is guests were attended the party is 50.

Problem 6 :

Three children each contributed toward a birthday present for their mother. The oldest contributed three times as much as the youngest, while the second oldest contributed 50 cents more than the youngest. If the present costs $10.50, how much did each contribute?

Solution :

Let x be the amount contributed by the youngest.

Amount contributed by oldest = 3x

Amount contributed by second oldest = 0.50

Amount in the present = 10.50

x + 3x + 0.50 = 10.50

4x = 10.50 - 0.50

4x = 10

x = 10/4

x = 2.5

Problem 7 :

At a school game, student tickets were 50 cents each and adult tickets were $1 each. If the total receipts from 900 tickets were $500, how many tickets of each kind were sold?

Solution :

Let x be the number of student tickets and 900 - x be the number of adult tickets.

Total number of tickets = 900

Total cost = 500

0.50x + 1(900 - x) = 500

0.50x + 900 - x = 500

-0.50x + 900 = 500

-0.50x = 500 - 900

-0.50x = -400

x = 400/0.50

x = 800

Number of student tickets = 800

number of adult tickets = 100

Problem 8 :

A salesman sold 200 pairs of slippers. Some were sold at $6 per pair and the remainder were sold at $11 per pair. Total receipts from this sale were $1600. How many pairs of slippers were sold at $6 each?

Solution :

Total number of pairs of slippers = 200

In which x be the number of slippers cost $6, then 200 - x number of slippers cost $11.

6x + (200 - x) 11 = 1600

6x + 2200 - 11x = 1600

-5x + 2200 = 1600

-5x = 1600 - 2200

-5x = -600

x = 600/5

x = 120

Number of slippers that cost $6 is 11.