Question

2.) You are buying gifts for 10 people. You decide to buy each person either a CD or a

DVD. A CD costs $12 and a DVD costs $20.
a. Let c = the number of CDs you decide to buy. Write an expression in terms of c
for the number of DVDs you buy.
b. Write an expression in terms of c for the cost of the CDs.
c. Write an expression in terms of c for the cost of the DVDs.
d. Write and simplify an expression in terms of c for the total cost of all the gifts you
buy.

Answer 1

a. The number of DVDs is 10 - c

b. The cost of the CDs is 12c

c. The cost of the DVDs is 20(10 - c)

d. The total cost of all gifts is 200 - 8c

Explanation:

* Lets explain how to solve the problem

- You are buying gifts for 10 people

# You will buy 10 gifts

- The gifts are CD or DVD

# The total numbers of CDs and DVDs is 10

- The cost of each CD is $12 and the cost of each DVD is $20

a.

# c is the number of CDs

∵ You buy c CDs

∵ The total numbers of CDs and DVDs is 10 as we said up

∴ c + the numbers of DVDs = 10

- Subtract c from both sides

∴ The number of DVDs = 10 - c

* The number of DVDs is 10 - c

b.

∵ The number if CDs is c

∵ The cost of each CD is $12

∴ The cost of the CDs = 12 × c = 12c

* The cost of the CDs is 12c

c.

∵ The number of DVDs is 10 - c

∵ The cost of each DVD is $20

∴ The cost of the DVDs = 20(10 - c)

* The cost of the DVDs is 20(10 - c)

d.

∵ The cost of the CDs is 12c

∵ The cost of the DVDs is 20(10 - c)

- The total cost of all the gifts is the sum of the costs of CDs and DVDs

∴ The total cost of all gifts = 12c + 20(10 - c)

- Multiply the bracket by 20

∵ 20(10 - c) = 100(2) - 20(c) = 200 - 20c

∴ The total cost of all gifts = 12c + 200 - 20c

- Add like terms

∴ The total cost of all gifts = 200 - 8c

* The total cost of all gifts is 200 - 8c