How many liters each of a 50% acid solution and a 85% acid solution must be used to produce 70 liters of a 75% acid solution? (Round to two decimal places if necessary.)

Answer 1

Let x = liters of 50% acid solution

y = liters of 85% acid solution

Note: the 50% acid solution is also 50% water; the 85% acid solution is also 15% water

One equation is easy:

x + y = 70 (total liters is 70)

Now either the amount of acid in one container + the amount of acid in the 2nd container equals the amount of acid in the final container:

.5 x + .85 y = 70(.75)

You can also do water plus water equals total water:

.5 x + .15 y = 70(.25) (the water in the final beaker is 25% water since it is 75% acid).

Let's use the 2nd equation and you can try it using the acid + acid equation to verify the results are the same.

x + y = 70

.5x + .15y = 70(.25)

Suggestion: multiply every term of the 2nd equation by 100 to clear the decimals:

50x + 15 y = 70(25)

Solve 1st equation for x or y and substitute into the 2nd):

y = 70 - x

50x + 15(70 - x) = 70(25)

50x - 15x + 70(15) = 70(25)

35x = 70(25) - 70(15)

35x = 70(25 - 15)

35 x = 700

x = 700/35 = 20

y = 70 - 20 = 50

So 20 liters of 50% solution and 50 liters of 85% acid solution.

Check:

.5(20) + .85(50)

10 + 42.5

52.5

And .75% of 70 liters is 52.5. Check!