Christine went shopping and bought each of her eight nephews a gift., either a video costing $14.95 or a cd costing $16.88. She spent $131.18 on the gifts. How many videos and how many cds did she buy?

Question

mathstudent55 · Answer

Let v = number of videos, and let c = number of cd's.

How many total videos and cd's did she buy?

tootsi123 · Answer

I have no clue..

mathstudent55 · Answer

You need to read the problem before you can answer it.
It says how many.

mathstudent55 · Answer

"Christine went shopping and bought each of her eight nephews a gift..."

tootsi123 · Answer

It says how much it costs?

mathstudent55 · Answer

We'll deal with the price later.
Now we are just dealing with the numbers of videos and cd's.

tootsi123 · Answer

Okay so she bought 8 items, that still doesnt help me ?

mathstudent55 · Answer

You are correct. It is 8.
It does help.

mathstudent55 · Answer

v is the number of videos.
c is the number of cd's.
We don;t know yet how many videos and how many cd's she bought, but we do know the total number she bought was 8.

That means we can write this equation:

v + c = 8

Ok so far?

tootsi123 · Answer

Yes.

mathstudent55 · Answer

Now we start thinking of prices and the amount of money spent.
If one video costs $14.95, how much do v videos cost?

tootsi123 · Answer

14.95

tootsi123 · Answer

14.95+16.88=131.18??

mathstudent55 · Answer

No. Just follow along.

14.95 is the price of 1 video.
v is the number of videos bought.

For example, let's say she bought 5 videos.
1 video costs 14.95. 
What operation would you do to find how much 5 videos cost?

tootsi123 · Answer

14.95+5=8?

mathstudent55 · Answer

No.

If 1 video costs 14.95, then
1 video costs 1 * 14.95
2 videos cost 2 * 14.95
3 videos cost 3 * 14.95
4 videos cost 4 * 14.95
etc.
You multiply the number of videos by how much each one costs to find the price of all the videos.
That means 5 videos cost 5 * 14.95

Since we don't know yet how many videos were bought, we are calling that number v.
Then, the price paid for all the videos bought is v (the number of videos bought) times $14.95.

2 videos cost 2 * 14.95
v videos cost v * 14.95, or 14.95v

tootsi123 · Answer

Okay

mathstudent55 · Answer

Each video costs 14.95.
v videos cost 14.95v

Now we do the same with the cd's
Each cd costs $16.88
Then c number of cd's cost 16.88c

tootsi123 · Answer

ok

mathstudent55 · Answer

The total amount spent, then, is 

$\sf \color{red}{the ~amount ~spent ~on ~videos}~ plus ~\color{green}{the ~amount ~spent ~on ~cd's}$

$\color{red}{~~~~~~~~~~~~~~~~~14.95v} ~~~~~~~~~~~~~~~~~~~~+ \color{green}{~~~~~~~~~~~~~16.88c}$

mathstudent55 · Answer

Without the colors, the amount spent is

14.95v + 16.88c

The problem tells us that the total amount spent was $131.18, that means that

14.95v + 16.88c must equal 131.88

That gives us the second equation:

14.95v + 16.88c = 131.88

mathstudent55 · Answer

Ok so far?

tootsi123 · Answer

yea

mathstudent55 · Answer

Now we need to use the two equations below as a system of equations and solve them to find v and c.

$v + c = 8$

$14.95v + 16.88c = 131.18$

mathstudent55 · Answer

Have you learned the substitution method of solving systems of equations?

tootsi123 · Answer

yea

tootsi123 · Answer

Thanks. I got it.

mathstudent55 · Answer

Solve the first equation for v:

c = 8 - v

Substitute 8 - v in for c in the second equation:

14.95v + 16.88(8 - v) = 131.18

14.95v + 135.04 - 16.88v = 131.18

-1.93v = 3.86

v = 2

Now substitute v = 2 in v + c = 8 to find c.