SOLVING WORD PROBLEMS USING DISTRIBUTIVE PROPERTY

Problem 1 :

Vanessa makes 7 identical flower arrangements for the tables at a banquet. Each arrangement contains some roses and 9 tulips. Vanessa uses a total of 147 flowers to make the arrangements. How many roses are in each arrangement?

Solution:

Let x represent the number of roses.

Then arrangement contains x + 9 flowers.

7(x + 9) = 147

Using distributive property, we get

7x + 63 = 147

7x = 84

x = 12

So, 12 roses are in each arrangement.

Problem 2 :

Five people visited a local restaurant to get some lunch. A burger costs 6 dollars and a bottle of apple juice costs 2 dollars. If all five people ordered a burger and a bottle of apple juice, write a numerical expression to show the amount of money the restaurant made for this order.

Solution:

Cost of burger = 6 dollars

Cost of apple juice = 2 dollars

Total cost restaurant made = 5(6 + 2)

Hence, 5(6 + 2) is required expression for total cost.

Problem 3 :

Each row in a classroom has 3 girls and 2 boys. There people 4 rows in that class. Write a numerical expression to show the number of students in that class.

Solution:

Number of girls = 3 

Number of boys = 2

Numerical expression

Number of students in that class = 4 × (3 + 2) 

= 4 × 5

= 20

Problem 4 :

Two men are trying to see how many computers they can build together in a month. One of the men was able to build 75 computers while the other was able to build 60. Write a numerical expression showing the number of computers both were able to build together.

Solution :

The numerical expression is 

75 + 60 = 135

= 15(5 + 4) [Distributive property]

This is the numerical expression showing the number of computer both were able to build together.

Problem 5 :

Mr.Vargas takes his class for 24 students ice skating. Each students pays an entrance fee to enter the rink and a $4 fee to rent skates. The total cost for the students to enter the rink and rent skates is $216. What is the ice skating entrance fee ?

Solution :

Let x be the number of entrance ticket.

Cost to rent skates = 4

Total cost spent by each student =  x + 4

Total number of students = 24

Cost spent by all 24 students = 216

24(x + 4) = 216

Using distributive property, we get

24x + 96 = 216

24x = 216 - 96

24x = 120

x = 120/24

x = 5

So, cost of each entrance ticket is $5.

Problem 6 :

A caterer is preparing a dinner for a party. She charges a flat of $16 plus $8.25 per person. Find the number of people at a dinner that costs $131.50

Solution :

Flat charge = 16

Cost per person = 8.25

Let x be the number of persons 

16 + 8.25x = 131.50

8.25x = 131.50 - 16

8.25x = 115.5

x = 115.5/8.25

x = 14

So, the number of people who attend the dinner is 14.

Problem 7 :

DE Andre is ordering tickets to a concert. He buys 3 tickets that all have the same price. There is a service charge of $4.75 per ticket. The total cost of his order is $111.75. What is the price of each ticket ?

Solution :

The service charge per ticket = 4.75

Total cost to this order = 111.75

Price per ticket = x

Number of tickets bought by him is 3.

3 (x + 4.75) = 111.75

3x + 14.25 = 111.75

3x = 111.75 - 14.25

3x = 97.50

x = 97.50/3

x = 32.50

So, price of each ticket is $32.50