A 70% salt solution was diluted with purified water to produce about 50 liters of 55% salt solution. Approximately how much purified water was used?

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Answer 1 · 2018-02-24T10:37:35

see a solution process below;

Let the amount of purified water used be $x$ $x$

Now interpreting the statement;

$70 % (50 - x) = 55 % (50)$ $70%(50 - x) = 55%(50)$

$\frac{70}{100} (50 - x) = \frac{55}{100} (50)$ $70/100(50 - x) = 55/100(50)$

$0.70 (50 - x) = 0.55 (50)$ $0.70(50 - x) = 0.55(50)$

$35 - 0.70 x = 27.5$ $35 - 0.70x = 27.5$

Collecting like terms..

$35 - 27.5 = 0.70 x$ $35 - 27.5 = 0.70x$

$7.5 = 0.70 x$ $7.5 = 0.70x$

Divide both sides by $0.70$ $0.70$

$\frac{7.5}{0.70} = \frac{0.70 x}{0.70}$ $7.5/0.70 = (0.70x)/0.70$

$x = \frac{7.5}{0.70}$ $x = 7.5/0.70$

$x = 10.7$ $x=10.7$

$x \approx 11 L$ $x ~~ 11L$

Hence the purified water was used is approximately $11 L$ $11L$