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March 30, 2017

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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.

  • Math - ,

    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.

  • Math - ,

    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?

  • Math - ,

    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?

  • Math - ,

    No.

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