Question

Phillip bought 12 used CDs and DVDs. CDs cost $2 each and DVDs cost $3 each. He spent $31 not including tax. How many DVDs did Phillip buy?

Answer 1

C + D = 12 and 2C + 3D = 31

Can you solve those 2 simultaneous equations now?

Answer 2

I suggest the elimination method. Take the first equation and multiply both sides by "-2". Take that new equation and add it to the 2nd equation, left side to left side and right to right. You will get "D".

Answer 3

After you've solved it that way, it's fun to think about how you could solve it in your head. What if all of the items purchased were CDs? That'd be 12 * $2 = $24. Hmm, not quite enough, what if we changed some of the CDs to DVDs? Each disk we change ups the expenditure by $3-$2 = $1. We were $31-$24=$7 short, so changing $7/$1 CDs to DVDs would give us the answer.

Amaze your friends not only with your ability to solve these problems, but also to instantly solve them without paper and pencil :-)

Answer 4

-2(C + D) = -2(12) -> -2C - 2D = -24

-2C - 2D = -24
2C + 3D = 31
------------
D = 7

Answer 5

oh i get it!

Answer 6

But whatever method you use to solve, it's important to test your solution in both equations to make sure it is correct. Checking just one isn't sufficient, as you can have a set of numbers that satisfies some equations without satisfying others.

7 DVD + 5 CDs = 12 total
7*3 + 5*2 = 21+10=31
so our solution is correct.

Answer 7

thank you @whpalmer4 and @tcarroll010

Answer 8

as an example of a solution that matches one but not the other:
9 DVDs + 2 CDs = 9*3 + 2*2 = 27+4=31
however 9+2 doesn't equal 12...

Answer 9

so the answer is 7 correct?

Answer 10

yes, 7 DVDs (and 5 CDs)

Answer 11

uw!