Question 1141587
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(1) Using the standard algebraic approach....<br>
8 L of 10%, plus x L of 5%, equals 8% of (8+x) L:<br>
{{{.10(8)+.05(x) = .08(8+x)}}}
{{{.8+.05x = .64+.08x}}}
{{{.16 = .03x}}}
{{{x = .16/.03 = 16/3}}}<br>
ANSWER: 16/3 L, or 5 1/3 L<br>
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A completely different method -- faster and easier, if you understand it....<br>
You are going from 10% towards 5%; you are stopping at 8%.<br>
8 is 2/5 of the way from 10 to 5.  (10-8=2; 10-5=5)<br>
That means 2/5 of the mixture is what you are adding; that means 3/5 of the mixture is what you started with; that means the amount you need to add is (2/5)/(3/5) = 2/3 of the amount you started with.<br>
ANSWER: (2/3)*8 = 16/3 L