To solve this problem, we can set up a system of equations using the following information:
Let x be the number of liters of the 80% acid solution.
Let y be the number of liters of the 40% acid solution.
Since the desired mixture is 10 liters, we have the equation:
x + y = 10
We also know that the acid percentage in the 10-liter mixture should be 48%. Therefore, the equation for the acid concentration is:
(80% * x + 40% * y) / 10 = 48%
Now we can solve this system of equations to find the values of x and y.
Let's start by rearranging the first equation to solve for x:
x = 10 - y
Now substitute this value of x in the second equation:
(80% * (10 - y) + 40% * y) / 10 = 48%
Simplifying this equation:
(8 - 0.8y + 0.4y) / 10 = 0.48
(8 - 0.4y) / 10 = 0.48
To eliminate the decimal point, multiply both sides of the equation by 10:
8 - 0.4y = 4.8
Now, isolate the term with y by subtracting 8 from both sides of the equation:
-0.4y = -3.2
Divide both sides of the equation by -0.4 to solve for y:
y = -3.2 / -0.4
y = 8
Now substitute the value of y back into the first equation to solve for x:
x = 10 - 8
x = 2
Therefore, the lab assistant should mix 2 liters of the 80% acid solution with 8 liters of the 40% acid solution to prepare a 10-liter mixture with a 48% acid concentration.