Question

how many liters each of a 60% acid solution and a 80% acid solution must be used to produce 80 liters of a 75% acid solution​

Answer 1

20 liters of 60% acid solution and 60 liters of 80% acid solution

Explanation:

Let the amount of 60% solution needed be "x", and

amount of 80% solution needed be "y"

Since we are making 80 liters of total solution, we can say:

x + y = 80

Now, from the original problem, we can write:

60% of x + 80% of y = 75% of 80

Converting percentages to decimals by dividing by 100 and writing the equation algebraically, we have:

0.6x + 0.8y = 0.75(80)

0.6x + 0.8y = 60

We can write 1st equation as:

x = 80 - y

Now we substitute this into 2nd equation and solve for y:

0.6x + 0.8y = 60

0.6(80 - y) + 0.8y = 60

48 - 0.6y + 0.8y = 60

0.2y = 12

y = 12/0.2

y = 60

Also, x is:

x = 80 - y

x = 80 - 60

x = 20

Thus, we need

20 liters of 60% acid solution and 60 liters of 80% acid solution