Question

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

What is basic logic to construct the linear equation

Answer 1

Total quantity of solution = 600 litres
Amount of acid in this solution = 600 L x 12 /100 = 72 litres of acid

Let the amount of 30% acid solution to be added = A
therefore amount of acid in this solution = A x 30/100 =0.3A

Now , the final mixture should have acid more than 15%
amount of acid in mixture > 15% of the total acid content

72 +0.3A > 15/100 (A +600)
72 +0.3 A > 0.15 (A+600)
72 +0.3A > 0.15 A + 90
0.3A -0.15 A > 90-72
0.15 A > 18
15 /100 (A) > 18
A> 18 x 100/15
A > 120 L

Now , the final mixture should have acid less than 18 %
amount of acid in mixture <18 % of the total acid content

72 +0.3A < 18/100 (A +600)
72 +0.3 A < 0.18 (A+600)
72 +0.3A < 0.18 A + 108
0.3A -0.18 A < 108-72
0.12 A < 36
12 /100 (A) < 36
A< 36 x 100/12
A < 300 L

A >120 but A <300

so 120< A< 300

so the amount of 30% acid solution to be added should be more than 120 L but less than 300 L