You are buying gifts for 10 people. You buy each person a cd or a DVD. A cd costs $10 and a DVD costs $20. Write and simplify an equation

Question

You are buying gifts for 10 people. You buy each person a cd or a DVD. A cd costs $10 and a DVD costs $20. Write and simplify an expression in terms of c for the total cost of all the gifts you buy

Answer 1

Since there are 10 people, if you bought x cds, that means you are left over with 10 - x dvds. For example 1 cd and 9 dvds, 2cds and 8 dvds...

The cost for the cds is 10x and the cost for the dvds is 20(10 - x).

 

So the total cost, or the cost functions is c = 10x + 20(10-x).

 

So if you ever found out what the total cost was, you could just replace c with that number and solve. For example, if you spent a total of $130, solve 130 = 10x + 20(10-x). This comes out to x=7cds and therefore 3 dvds.

 

Until you have that specific number though, the best you can do is write that total cost function.

 

Hope this helped.

Answer 2

While Virginia is right that for an exact answer you need additional information, we can right a simple equation with what we have.  First off, we know that the total amount spend is the sum of the amount we spend on each the CDs and the DVDs, which are $10 and $20 a piece respectively.  We also know that there are only 10 gifts in total, which means that if we buy 4 CDs, then we only need 6 DVDs (10-4=6).  Re-writing these two pieces of information, we get:

 

Total Price = $10 * (Number of CDs) + $20 * (Number of DVDs)

 

and

 

10 = Number of CDs + Number of DVDs

 

At this point, you need to decide whether you want your equation in terms of the number of CDs purchased, or the number of DVDs purchased.  You will move the other variable to the same side of the equals sign as the 10, and substitute it into the first equation, giving you: 

 

Total Price = $10 * (Number of CDs) + $20 * (10 - Number of CDs)

 

or

 

Total Price = $10 * (10 - Number of DVDs) + $20 * (Number of DVDs)

 

Both equations give the same answer, you just are entering the information differently.  They can both be simplified, which I will leave to you, and you can use any variables you choose, such as p for Total Price, c for CDs and D for DVDs.