Theresa morgan a chemist has a 10% hydrochloric acid solution and a 65% hydrochloric acid solution. how many liters of each should she mix to get 1870 liters of a hydrochloric acid solution with 60% acid concentration

ANSWER:

170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.

SOLUTION:

First, set up a table. Fill in the unknowns with variables x and y. The table is attached below

From this, we can easily set up the two equations.  

Sum of values of two acids = Value of mixture  

0.1x + 0.65y = 1122  

For convenience, we'll multiply the entire equation by 100,

10x + 65y = 112200   ------ (1)  

Now, Sum of amounts of each acid = Amount of mixture  

x + y = 1870  ---------(2)

multiply (2) with 10 for easy calculation and derive the equation into one variable.

10x + 10y = 18700  

Subtracting equation (2) from (1),  

( + ) 10x + 65y = 112200

( − ) 10x + 10y = 18700

we get the solution as,

0 + 55y = 93500

Thus, 55y = 93500

y = 1700

Substituting y = 1700 in (2),

x + 1700 = 1870  

x  = 1870 - 1700  

x  = 170  

So, we have x = 170 and y = 1700

We can conclude that 170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution  to obtain 1870 liters of 60% solution.