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.

Question

Write and simplify an expression in terms of c for the total cost of all the gifts you buy.

My answer- My expression is 12c + 20(10-c). When I use the distributive property, I get 12c + 200 - 20c. Now, when I simplify this even further, I get 32c + 200, which is not making sense.

Answer 1

you should subtract that 20c, making

200-8c

note if c=0 all gifts are dvd's, costing 200.

Then since cd's are $8 cheaper, you save $8 for each cd bought.

Answer 2

Thank you. Also, the problem asks about what properties of real numbers I used to solve this problem. So far, I am only seeing the distributive property. Is this the only one used?

Answer 3

I suppose associative is also involved, since we have to use it to rearrange the

12c+200-20c
to be

200+12c-20c
then distributive again to get

200+(12-20)c

do you have some property that equates adding a negative and subtracting a positive?

Answer 4

No.