Virginia and Campbell had 100 kilograms of a 20% glycol solution. How much of a 40% glycol solution should be added to get a solution that is 35% glycol?

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Virginia and Campbell had 100 kilograms of a 20% glycol solution. How much of a 40% glycol solution should be added to get a solution that is 35% glycol?

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Answer 1 · 2015-10-09T19:46:05

$33 \frac{1}{3}$ $33 1/3$ kgm

Explanation:

Suppose we need to add $x$ $color(red)(x)$ kgm of $40 %$ $color(red)(40%)$ glycol to the $100$ $color(blue)(100)$ kgm of $20 %$ $color(blue)(20%)$ glycol solution

The resulting mass would be $(100 + x)$ $color(green)((100+x))$ kgm (at a concentration of $25 %$ $color(green)(25%)$ )

$20 % \times 100 + 40 % \times x = 25 % \times (100 + x)$ $color(blue)(20% xx 100) + color(red)(40% xx x) = color(green)(25% xx (100+x))$

$\Rightarrow XX 20 + \frac{2}{5} x = 25 + \frac{1}{4} x$ $rArrcolor(white)("XX")color(blue)(20)+color(red)(2/5x) = color(green)(25+1/4x)$

$\Rightarrow XX (\frac{2}{5} - \frac{1}{4}) x = 25 - 20$ $rArrcolor(white)("XX")(color(red)(2/5)-color(green)(1/4))x = color(green)(25)-color(blue)(20)$

$\Rightarrow XX \frac{3}{20} x = 5$ $rArrcolor(white)("XX")3/20x= 5$

$\Rightarrow XX x = \frac{100}{3} = 33 \frac{1}{3}$ $rArrcolor(white)("XX")x=100/3 = 33 1/3$

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Virginia and Campbell had 100 kilograms of a 20% glycol solution. How much of a 40% glycol solution should be added to get a solution that is 35% glycol?

1 Answer

Explanation:

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