Question

Gave a nuclear physicist needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he need to make the needed 30 liters of 60% acid solution?

Answer 1

Formulating a system of equations for this situation we have:

0.4(A)+0.7(B)=0.6(30) Equation(1)

A+B= 30 Equation(2)

A: Liters of 40% acid solution

B: Liters of 70% acid solution

0.4: 40%

0.7: 70 %

0.6: 60%

30 Liters of the third solution

Using the substitution method to solve the system,we have:

B= 30 - A Equation(2) (Subtracting A from both sides of the equation)

0.4(A) + 0.7(30 - A) = 18 Equation(1) (Substituting B=30-A in the equation 1)

0.4A + 21 - 0.7A = 18 (Distributing)

0.4A - 0.7A = -3 (Subtracting 21 from both sides of the equation)

-0.3A= -3 (Subtracting like terms)

A= 10 (Dividing by -0.3 on both sides of the equation)

B= 30 - 10 = 20 (Replacing A=10 in the equation 2)

Answers:

He needs 10 liters of 40% acid solution

He needs 20 liters of 70% acid solution