Question

A manufacturer has 600 liters of a 12% solution of acid. How many liters of a 30% acid solution must be added to it so that the acid content in the resulting mixture will be more than 15% but less than 18%?

(a) 200 liters
(b) 250 liters
(c) 300 liters
(d) 350 liters

Answer 1

To achieve an acid concentration more than 15% but less than 18%, the manufacturer needs to add 300 liters of a 30% acid solution to the existing 600 liters of 12% acid solution. Option C is the correct answer.

Step-by-step explanation:

The question involves the concept of mixtures and concentration in chemistry interpreted through mathematics. The student has 600 liters of 12% acid solution and wants to add a certain amount of 30% acid solution so that the resulting mixture has an acid concentration of more than 15% but less than 18%. Let's define x as the amount of 30% solution needed. We can set up an inequality to represent the concentration of the final mixture:

0.12(600) + 0.30(x) > 0.15(600+x)

0.12(600) + 0.30(x) < 0.18(600+x)

Solving the inequality:

• For the lower limit (15%):
  
• For the upper limit (18%):
  

Combining the two inequalities, we find that 120 < x < 300. Hence the correct option is (c) 300 liters, as it is the only value that satisfies the condition.