lisa is starting a movie collecion. blu-rays cost $20 each and DVD's cost $14 each. If she buys 12 movies for $186, how many movie did she buy?

Guest
May 18, 2017

#1
**+1 **

Call the number of $20 movies, x

Then the number of $14 movies = 12 - x

And we have

20x + 14 (12 - x) = 186 simplify

20x + 168 - 14x = 186

6x + 168 = 186 subtract 168 from both sides

6x = 18 divde both sides by 6

x = 3 = number of $20 movies

And 12 - 3 = 9 = the number of $14 movies

CPhill
May 18, 2017

#2
**+1 **

Let 'b' represent the number of Blue Rays

Since she bought 12 movies, we know that the number of DVDs is '12 - b'

So b + (12 - b) = 12

She spent $186, and the price of Blue Rays are $20 while DVDs are $14

So 20b + 14(12 - b) = 186

To find b, lets make the coefficient of b equal 20 in both equations

(b + (12 - b) = 12) * 20

20b + 20(12 - b) = 240

Now lets subtract the second equation from the first one.

20b + 20(12 - b) = 240

- 20b + 14(12 - b) = 186

-------------------------------

6(12 - b) = 54

6(12 - b) = 54

72 - 6b = 54

72 - 54 = 6b

(18 = 6b) / 6

3 = b

We now know that there are 3 Blue Rays

And since the number of DVDs is 12 - b, we know that there are 9 DVDs

So therefore, Lisa bought 3 Blue Rays and 9 DVDs for $186

Guest
May 18, 2017