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

I love explaining these. Are you ready to learn sir/madam?

Answer 2

Yes

Answer 3

Alright. There are 2 unknowns here correct? Tell me what they are.

Answer 4

how many cds he bought and how many dvds he bought I'm guessing

Answer 5

Yes. For now, we'll call the number of CDs by the variable, C. and the number of DVDs will be D.

Answer 6

Alright sounds good

Answer 7

Using those variables, express the total number of CDs and DVDs he bought.

Answer 8

12

Answer 9

Use the variables in an equation.

Answer 10

C + D = 31

Answer 11

Incorrect.

What we want is

(the number of CDs) + (the number of DVDs) = 12

Answer 12

2C + 3D = 12

Answer 13

You are getting ahead of yourself.

Answer 14

What is the variable for (number of CDs)?

Answer 15

C?

Answer 16

Yes. We already named it.

So if we know

(the number of CDs) + (the number of DVDs) =12

Write an equation using variables.

Answer 17

C + D = 12?

Answer 18

Correct. That's the first part of the story problem. Now for part 2!

How much does a CD cost?
How much does a DVD cost?

Answer 19

2$ and 3$

Answer 20

So if he bought 3 CDs what would the price be?

Answer 21

6$

Answer 22

Good. And we get that by (the price of a CD)x(the number of CD)

or 2C

Answer 23

So let's write an equation to find the total price of everything altogether. We know it's $31

Answer 24

Right so 2C + 3D = 31?

Answer 25

Yes! Now we have 2 equations

C+D=12

and

2C + 3D =31

Answer 26

Now for the fun stuff.

If C + D =12 ,

then what does D equal?

Answer 27

3?

Answer 28

Don't guess.

Answer 29

If C + D = 12

then D = 12 - C

Answer 30

TO get that, we would just subtract C on both sides of the equal sign.

Answer 31

ok got it

Answer 32

Alright so now we know what D equals. We want to substitute it into the second equation.

2C + 3D = 31

2C + 3(12-C) =31

Answer 33

2C-36+3C=31
2C+3C=31+36
5C=67

Answer 34

You have to do that one again. I accidentally wrote it incorrectly.

Answer 35

It is +3D

so it should be 3(12-C)

Answer 36

so wait the 2D is in front so it should be
2D + 3(12-7) = 31?

Answer 37

Where are you getting 7 from?

You should be working on solving this

2C + 3(12-C) =31

Answer 38

whoops sorry i meant c

Answer 39

Go ahead and solve that equation for C

Answer 40

2C + 3(12-C) =31
2C + 36 - 3C = 31
2C - 3C = 31-36
-1C=-5

Answer 41

Finish solving.

Right now you have -C=-5

Solve so it says C=????

Answer 42

5

Answer 43

:D

So C=5

Answer 44

So the number of CDs is what?

Answer 45

5

Answer 46

Alright. Knowing what C is, can you solve for D?

Answer 47

C+D=12
5+D=12
D=12-5
D=7

Answer 48

So the answer that the problem asks you for is??????

Answer 49

How many DVDs did Phillip buy. which is 7

Answer 50

Congrats!

Feel free to check your answer by plugging in 5 for C and 7 for D in the second equation.

Answer 51

Yay thank you very much for your help :)