WORD PROBLEMS ON FUNDAMENTAL OPERATIONS

Problem 1 :

There are 3 senior managers 6 junior managers in a company. Each senior manager has 3 personal assistants nurses and each junior manager has 2 personal assistants. How many personal assistants are working in the company?

Solution :

Number of personal assistants working in the company :

= 3x3 + 6x2

= 9 + 18

= 27

Problem 2 :

A box of crayons contains 40 crayons, a box of pencils contains 28 pencils and a box of erasers contains 18 erasers. Alex bought half of a box of crayons, one-fourth of a box of pencils and one-third of a box of erasers. Find the total number of items he bought. 

Solution :

Total number of items :

= (1/2)(40) + (1/4)(28) + (1/3)(18)

= 20 + 14 + 6

= 40

Problem 3 :

Angelina has $250. If Mia has $55 more than twice of the money Angelina has, find the amount of money Mia has. 

Solution :

Amount of money Mia has :

= 2(250) + 55

= 500 + 55

= $555 

Problem 4 :

There are 3 managers and 1 general manager in a firm. There are 4 assistant managers for each manager and there are 5 personal assistants for each assistant manager. If each personal assistant controls 10 employees, find the total number of people working in the office.

Solution :

Number of people working in each category :

General manager : 1

Number of managers : 3

Number of assistant managers : 3 x 4 = 12

Number of personal assistants : 12 x 5 = 60

Number of employees : 60 x 10 = 600

Total number of people working in the company :

= 1 + 3 + 12 + 60 + 600

= 676

Problem 5 :

Gian had some money. He gave three-fourth of the money to his mother. He spent three-fourth of the remaining for his monthly expanses and donated the rest to a charity. If Gian originally had $9000, find the amount money he donated to the charity.

Solution :

Given : Gian had $9000 and he gave three-fourth of the money to his mother.

Remaining = 9000 - (3/4)9000

= 9000 - (0.75)9000

= 9000 - 6750

= 2250

Given : Gian spent three-fourth of the remaining for his monthly expanses and donated the rest to a charity.

Amount of money James donated to the charity :

= (1/4)2250

= (0.25)2250

$562.50

Problem 6 :

The numerator of a fraction is 3 less than the denominator. If 2 be added to both numerator and denominator, the fraction becomes 2/3. Find the fraction.

Solution :

Let x be the denomitor of the fraction.

Then, the numerator is (x - 3).

Then, the fraction is

(x - 3)/x

Given : If 2 be added to both numerator and denominator, the fraction becomes 4/7.

(x - 3 + 2)/(x + 2) = 2/3

(x - 1)/(x + 2) = 2/3

3(x - 1) = 2(x + 2)

3x - 3 = 2x + 4

Subtract 2x from both sides.

x - 3 = 4

Add 3 to both sides.

x = 7

Therefore, the fraction is

= (7 - 3)/7

= 4/7

Problem 7 :

To become a journalist, Daniel has to write notes at a rate of 100 words per minute. Now, Daniel writes 80 word per minute, but through practice, he can increase his speed by 2 words per minute each week. Find the number of words per minute that Daniel can write in 4 weeks.

Solution :

Number of words per minute that Daniel can write in 4 weeks :

= 80 + 2x4

= 80 + 8

= 88

Problem 8 :

A taxi service charges $40 for the 10 miles and $2.50 for each additional mile. If James travels in the taxi for 13 miles, find the amount he has to pay.

Solution :

Amount has to be paid by James for 13 miles :

= 40 + (10 - 13)x2.50

= 40 + 3x2.50

= 40 + 7.50

= $47.50

Problem 9 :

An aquarium is partially filled and it contains 25 gallons of water. If a hose is turned on and water flows into the tank through a hose at a rate of 4 gallons per minute, find the amount of water in the aquarium after 40 minutes.

Solution :

Amount of water in the aquarium :

= 25 + 40(4)

= 25 + 160

= 185 gallons

Problem 10 :

Adam spent $ for his trip to New York. The money $1800 he spent covers travelling expense, staying in hotel and food. Adam spent $800 for traveling, $150 per day for staying in a hotel and the rest for food. If he had stayed for 4 days, find the amount of money he spent for food.

Solution :

Amount of money spent only for food :

= 1800 - 800 - 4(150)

= 1800 - 800 - 600

= 1800 - 1400

= $400

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.