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AURORKA [14]
3 years ago
5

One antifreeze solution is 31% alcohol and another is 15% alcohol. How much of each mixture should be added to make 28 L a solut

ion that is 27% alcohol ?
Mathematics
1 answer:
USPshnik [31]3 years ago
7 0

Let

<em>x</em> = volume of the 31% solution

<em>y</em> = volume of the 15% solution

We want a solution with a total volume of 28 L, so

<em>x</em> + <em>y</em> = 28

For each liter of either solution, there is a contribution of 0.31 L and 0.15 L of alcohol, respectively. In the resulting solution, we want a concentration of 27% alcohol, which comes out to 0.27 * 28 L = 7.56 L. So

0.31 <em>x</em> + 0.15 <em>y</em> = 7.56

The first equation says

<em>y</em> = 28 - <em>x</em>

Substitute this into the second equation and solve for <em>x</em>, then for <em>y </em>:

0.31 <em>x</em> + 0.15 (28 - <em>x</em>) = 7.56

0.31 <em>x</em> + 4.2 - 0.15 <em>x</em> = 7.56

0.16 <em>x</em> = 3.36

<em>x </em>= 21

<em>y</em> = 28 - <em>x</em>

<em>y</em> = 7

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