% solution

[jenn2998]

a chemist needs to mix a 18% acid solution with a 45% acid solution ti obtain 12 liters of a 36% acid solution. how many liters of each of the acid solutions must be used?

 

[Loren]

Picture 3 vats. One vat has x liters of 18% acid. The second vat has y liters of 45% acid. The third vat is empty, but will contain 12 liters of the new mixture.
Build two equations. One equation is based on how many liters of the 18% solution is combined with the number of liters of the 45% solution to get 12 liters of the new mixture.
The second equation is simply the amount of acid in the 18% solution plus the amount of acid in the 45% solution equals the amount of acit in the 36% solution. Hint: The amount of acid in the 18% solution is 0.18x.
If you need more help, show us how far you got, so we know where you are stuck.

 

[Denis]

a liters : x%
b liters : y%
=============
(a+b) liters: z%

z = (ax + by) / (a + b)

 

[soroban]

Hello, jenn2998!

Here's how I baby-talk my way through these Mixture Problems . . .

A chemist needs to mix a 18% acid solution with a 45% acid solution
to obtain 12 liters of a 36% acid solution.
How many liters of each of the acid solutions must be used?

Consider the amount of acid in the solutions.

$\displaystyle \text{Let } x\text{ = amount of the 18 percent solution.}$
. . $\displaystyle \text{It contains: }\:\text{18 percent} \times x \:=\:0.18x \text{ liters of acid.}$

$\displaystyle \text{Then }12-x\text{ = amount of the 45 percent solution.}$
. . $\displaystyle \text{It contains: }\:\text{45 percent} \times (12-x) \:=\:0.45(12-x)\text{ liters of acid.}$

. . $\displaystyle \text{The final mixture contains: }\:0.18x + 0.45(12-x)\text{ liters of acid.}$ .[1]


$\displaystyle \text{But we know that the final mixture will be: 12 liters which is 36 percent acid.}$
. . $\displaystyle \text{It will contains: }\:0.36 \times 12 \:=\:4.32\text{ liters of acid.}$ .[2]


$\displaystyle \text{We just described the final amount of acid in }two\text{ ways.}$


\(\displaystyle There\text{ is our equation! }\quad\hdots\quad 0.18x + 0.45(12-x) \:=\:4.32\)


Go for it!