Problem 1 :
The Valley High School Auditorium is able to seat 8 elementary school groups of 65 students. Use the Distributive Property to determine how many students they can seat.
Solution:
If there are 8 groups of students.
= 8 × (60 + 5)
= 8 × 60 + 8 × 5
= 480 + 40
= 520 students
They can seat 520 students.
Problem 2 :
Five friends each buy a shirt that costs x dollars and a pair of shoes that cost $24.00. Write an expression to show how much total money they spent. Then rewrite the expression using the Distributive Property.
Solution:
Total cost of shirt and shoes = (24 + x)
Total money spent = 5 × (24 + x)
Total money spent = (5 × 24) + (5 × x)
= 5x + 120
Problem 3 :
A rental company buys 7 more compact cars for $8,500 each and 7 more midsize cars for $12,500 each. How much total money will they spend?
Solution:
Total money spent = 7 × (8500 + 12500)
= 7 × 21000
=147000
They spent 147000 dollars.
Problem 4 :
A baking company charges $1.75 per slice for baking and $0.35 per slice for decorating. How much would a decorated cake cost containing 150 slices?
Solution:
Total cost = 150 × (1.75 + 0.35)
= 150 × 2.1
= 315
A decorated cake would cost 315 dollar containing 150 slices.
Use the table that shows the umber of seats available on various types of aircrafts.
Problem 5 :
How many total seats will the airline gain by purchasing three more of both the 737 aircrafts and MD-88 aircrafts?
Solution:
Total number of seats in three 737 aircrafts = 3 × 150 = 450
Total number of seats in three MD-88 aircrafts = 3 × 142 = 426
= 450 + 426
Total number of seats gained is 876 seats.
Problem 6 :
How many more people can sit on four 777 aircrafts than on four 767 aircrafts?
Solution:
Number of seats in four 777 aircrafts = 268 × 4 = 1072
Number of seats in four 767 aircrafts = 250 × 4 = 1000
= 1072 − 1000
72 many more people can sit on four 777 aircrafts than on four 767 aircrafts.
Problem 7 :
The price for each textbook is p. The number of notebooks bought by Lily, Jim and Jessica is a, b and c. Write an expression to represent the total cost of all the notebooks bought by 3 people.
Solution :
Price of each text book = p
Number of books bought by Lily = a
Number of books bought by Jim = b
Number of books bought by Jessica = c
Total number of books = a + b + c
Total cost = p(a + b + c)
Problem 8 :
The price each meter of wire is u, and there are 3 parts of wires whose length are x, y and z. Write the expression which represents the cost of buying the 3 parts of wire.
Solution :
Price of each meter of wire = u
Length of three parts of wire are x, y and x.
Cost of buying 3 parts = u(x + y + z)
Problem 9 :
For two days, your boss decides to double the commission on what you sell. If on day 1, you make f dollars in commission and and day 2, you make g dollars in commission, write an expression for the total commission you earn.
Solution :
Sales made on day 1 = f
Sales made on day 2 = g
Total sales = f + g
Total commission = 2(f + g)
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