A lab technician needs 25 liters of a solution that is 15% acid for a certain experiment , but she has only a solution that is 10% acid and a solution that is 30% acid . How many liters of the 10% and the 30% solutions should she mix to get what she needs?

The correct answer is: 18.75 liters of the 10% and 6.25liters of 30% acid solutions should be mixed by the lab technician to get what she needs.

Step-by-step solution:-
Let the quantity of 10% acid solution and 30% acid solution required be x liters and y liters, respectively.
∴ Total quantity of acid obtained by mixing the 2 liquids = x + y ............................................................................ (Equation i)
Total quantity of acid required by the lab technician = 25 liters .......................................................................... (Given)
∴ Total quantity of acid required by the lab technician = 25 ................................................................................... (Equation ii)
We need to find the quantity of both the liquids that matches the total quantity required by the lab technician.
∴ Equating Equations i & ii, we get-
x + y = 25 ........................................................................................................................................................ (Equation iii)
Total acid solution content obtained by mixing the two types of liquid = 10/100 * x + 30/100 * y
∴ Total acid solution content obtained by mixing the two types of liquid = 0.1x + 0.3y ..................................... (Equation iv)
Total acid solution content required by the lab technician = 15/100 * 25 liters .............................................. (Given)
∴ Total acid solution content required by the lab technician = 3.75 ...................................................................... (Equation v)
We need to find the quantity of both the liquids that matches the acid solution content required by the lab technician.
∴ Equating Equations iv & v, we get-
0.1x + 0.3y = 3.75 ...................................................................................................................................................... (Equation vi)
Multiplying Equation iii by 0.1, we get-
x + y = 25 ...................................................................................................................................................... (Equation iii)
∴ 0.1x + 0.1y = 0.1 * 25
∴ 0.1x + 0.1y = 2.5 ................................................................................................................................................. (Equation vii)
Final Answer:-
∴ 18.75 liters of the 10% and 6.25liters of 30% acid solutions should be mixed by the lab technician to get what she needs.