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olasank [31]
3 years ago
14

Sandra needs to make 500 L hand sanitizer with 75% alcoholic solution. He has only two of the alcoholic solutions available, a 6

5% solution and a 90% solution. How many litres of each alcoholic solution should he mix?
Mathematics
1 answer:
shtirl [24]3 years ago
8 0

If Sandra mixes <em>x</em> L of 65% solution with <em>y</em> L of 90% solution, then the resulting mixture has a total volume of

<em>x</em> + <em>y</em> = 500

litres, and it contains

0.65<em>x</em> + 0.90<em>y</em> = 0.75 (500) = 375

litres of alcohol.

Solve the first equation for <em>y</em> :

<em>y</em> = 500 - <em>x</em>

<em />

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

0.65<em>x</em> + 0.90 (500 - <em>x</em>) = 375

0.65<em>x</em> + 450 - 0.90<em>x</em> = 375

75 = 0.25<em>x</em>

<em>x</em> = 300

Solve for <em>y</em> :

<em>y</em> = 500 - 300

<em>y</em> = 200

So, Sandra should mix 300 L of 65% solution with 200 L of 90% solution.

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