Question 207890: this is the given problem: Solution X is 2% alcohol and solution Y is 6% alcohol. A drugstore owner wants to mix them in order to get a 60-L of solution that is 3.2% alcohol. How many liters of each should the owner use?
Solution:
Let x = the number of liters of X
y = the number of liters of Y
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+ solution + solution + mixture +
+ X + Y + +
---------------------+-------------+------------+---------------+
amt. of solution(L) + x + y + 60 +
---------------------+-------------+------------+---------------+
percent of alcohol + 2% + 6% + 3.2% +
---------------------+-------------+------------+---------------+
amt. of alcohol in + 0.02% + 0.06% + 0.032(60)or + 0.02x + 0.06y
the mixture(L) + + + 1.92 + = 1.9
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note: to get the amount of a alcohol, we multiply the amount of solution by the percentages.
equations:
(1) x + y = 60
(2) 0.02x + 0.06y = 1.92
multiplying eq.(2) by 100, we now have this system:
(1) x + y = 60
(2)2x +6y = 192
solving the system using elimination, we first multiply eq. by -2 and add the result to eq. (2)
-2x-2y =-120
2x+6y = 192
------------
4y = 72
y = 18
solving for x, we substitute 18 in place of y in eq. (1)
x + 18 = 60
x = 42
Please help me why it was multiplied by negative 2, and where this -2 came from?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! (1) x + y = 60
(2)2x +6y = 192
The second equation has a 2x, while the first equation has only x. You need to make the x terms subtract out, so in order to subtract out the 2x, you need a -2x. To get that, you have to multiply the first equation by -2. You could also have eliminated the y terms by multiplying the first equation by -6. We usually try to eliminate using the smaller number.
R^2
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