WORD PROBLEMS ON ORDER OF OPERATIONS

Problem 1 :

A certain small factory employs 98 workers. Of these, 10 receive a wage of $150 per day and the rest receive $85.50 per day. To the management, a week is equal to 6 working days. How much does the factory pay out for each week?

Solution :

Total number of workers = 98

Number of workers who are receiving $150 per day = 10

Number of workers who are receiving $85.50 per day = 88

Number of working days of the factory = 6

= 6 (10 x 150 + 88 x 85.50)

= 6(1500 + 7524)

= 6(9024)

= 54144

Problem 2 :

If the same factory has supplies expenses of $1135.78 a day in addition to the wages above and makes $60,128.72 in a week, what is the factory’s total profit or loss in one week?

Solution :

For wages, the company spends = 60128.72

Expenses per day = 1135.78

Total expenses for 6 days = 6(1135.78)

Expression :

= 60128.72 - (54144 + 6(1135.78))

= 60128.72 - (54144 + 6814.68)

= 60128.72 - 60958.68

= -829.96

So, it is loss.

Problem 3 :

A certain Math Club makes 35 bars of laundry soap a week and sells these at $20 each. Before the soap can all be sold, the pupils found out that 6 bars were destroyed by mice. How much will be the total sale at the end of a four-week month? Write an expression and show your work and answer.

Solution :

Number of soaps = 35

Selling price of each soap = 20

Number of soaps destroyed by mice = 6

Amount he may receive if the mice is not destroying

= 35 x 20

= 700

Amount destroyed by the mice = 6 x 20

= 120

Total sale = 700 - 120

= 580

Problem 4 :

Emily had 30 cookies to bring to school for her birthday. Three students wanted two cookies each. Then, a new student came to the school that day and he wanted three cookies. Then, one of the three kids gave their two cookies back. Emily was still passing out cookies. How many cookies did Emily have left to pass out after the students gave theirs back?

Solution :

= 30 - [3(2) + 1(3)] + 2

= 30 - [6 + 3] + 2

= 30 - 9 + 2

= 32 - 9

= 23

Emily will have 23 cookies.

Problem 5 :

Lilia scores 15 points fewer than Bob, who scores 35 points. Carol scores half as many points as Lilia. How many points does Carol score? Write an expression and evaluate it.

Solution :

Points scored by Bob = 35

Points scored by Lilia = 35 - 15 ==> 20

Points scored by Carol = 20/2 ==> 10

Expression :

(35 - 15) / 2

Problem 6 :

The King family went out to eat. They ordered three combo meals, two sodas, and one iced tea. Write an expression representing their bill. Then, determine the cost of the dinner for the entire family.

Solution :

Number of meals ordered = 3

Number of sodas = 2

Number of iced teas = 1

Expression :

= 3 (5.25) + 2 (2) + 1 (2.25)

= 15.75 + 4 + 2.25

= 22

So, the entire family has to spend $22.

Problem 7 :

The diagram shows landing zones for skydivers. Zone 1 is for experts. The remaining space is divided in half and designated as Zones 2 and 3 for tandem divers. What is the area of Zone 2?

Solution :

The given shape is square, by subtracting area of zone 1 from area of square, we get area of zone 2 and zone 3. Which are equal.

Area of zone = 1/2(Area of square - area of zone 1)

= 1/2 (40² - 20²)

= 1/2(1600 - 400)

= 1/2 x 1200

= 600 square yards

So, the area of the zone 2 is 600 square yards.

Problem 8 :

A square plot of land has side lengths of 40 meters. An archaeologist divides the land into 64 equal parts. What is the area of each part?

Solution :

Side length of square plot = 40 meter

Area of square plot = 40²

= 1600 square meter

It is being divided into 64 equal parts, then area of each part 

= 1600/64

= 25

Area of each part is 25 square meter.

Problem 9 :

A glass block window is made of two diff erent-sized glass squares. The window has side lengths of 40 inches. The large glass squares have side lengths of 10 inches. Find the total area of the small glass squares.

Solution :

Area of window = Area of large glass of squares + Area of small glass of squares

40² = 10² + area of small glass of squares

area of small glass of squares = 40² - 10²

= 1600 - 100

= 1500

Problem 10 :

A square vegetable garden has side lengths of 12 feet. You plant flowers in the center portion as shown. You divide the remaining space into 4 equal sections and plant tomatoes, onions, zucchini, and peppers. What is the area of the onion section?

Solution :

Area of onion section = 1/4 (Area of square vegetable garden - area of flower section)

= 1/4(12² - 4²)

= (1/4) (144 - 16)

= (1/4)(128)

= 32 square feet

So, area of onion section is 32 square feet.