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.

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

Step-by-step 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