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.
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.
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.
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?
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?
No.
Your initial expression is correct: 12c + 20(10-c). Now let's simplify it step by step.
First, distribute the 20:
12c + 200 - 20c
Next, combine like terms:
(12c - 20c) + 200
Simplifying further:
-8c + 200
So, the simplified expression in terms of c for the total cost of all the gifts is -8c + 200.
It's worth noting that the negative coefficient (-8) means the expression represents a decreasing function, which suggests that the total cost decreases as the number of CDs (c) increases. This may seem counterintuitive, but it's because the cost of CDs is less than the cost of DVDs.