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3 years ago

How much of 30% HCI and 45% HCI would be needed to mix and produce 50 liters of 35% HCI

Mathematics

1 answer:

VladimirAG [237]3 years ago

5 0

Answer:

33 1/3 liters of 30%
16 2/3 liters of 45%

Step-by-step explanation:

Let x represent the liters of 45% solution needed. Then the amount of HCl in the mix is ...

0.45x +0.30(50 -x) = 0.35(50)

0.15x = 0.05(50) . . . . . simplify, subtract 0.30(50)

x = (0.05/0.15)(50) = 50/3 = 16 2/3 . . . liters of 45% HCl

33 1/3 liters of 30% and 16 2/3 liters of 45% HCl are needed.

_____

<em>Comment on the solution</em>

You may notice that the general solution to a mixture problem of this sort is that the fraction of the mix that is the highest contributor is ...

(mix % - low %) / (high % - low %) = (.35 -.30) / (.45 -.30) = .05/.15 = 1/3

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Therefore, the transition matrix is given by

$T=\left[\begin{array}{ccc}-1&3\\2&4\end{array}\right] .$

Thus, the required matrix is

$T=\left[\begin{array}{ccc}-1&3\\2&4\end{array}\right] .$

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3 years ago

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