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?
+128474 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
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
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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
