How many liters each of 25​% and 10​% acid should be mixed to obtain 15 liters of 12​% ​acid?

Kind of Solution
Liters of Solution
Amount of Pure Acid
0.25
x
0.1
y
0.12
15

1 answer

Let's label the amount of 25% acid as x and the amount of 10% acid as y.

We want to find the values of x and y that satisfy the equation:

0.25x + 0.1y = 0.12(15)

This equation represents the total amount of pure acid in the mixture.
Let's solve for x:

0.25x + 0.1y = 1.8

Multiply both sides of the equation by 100 to get rid of the decimals:

25x + 10y = 180

Now let's solve for y in terms of x:

y = (180 - 25x)/10

We also know that the total amount of the mixture is 15 liters, so:

x + y = 15

Substituting the expression for y:

x + (180 - 25x)/10 = 15

Multiplying both sides of the equation by 10 to get rid of the fraction:

10x + 180 - 25x = 150

Combine like terms:

-15x = -30

Divide both sides of the equation by -15:

x = 2

Now let's substitute this value of x back into the equation for y:

y = (180 - 25(2))/10 = (180 - 50)/10 = 13

Therefore, we need 2 liters of 25% acid and 13 liters of 10% acid to obtain 15 liters of 12% acid.