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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
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 #1
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+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

 

 

cool cool cool

CPhill  May 18, 2017
 #2
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+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

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