A manufacturer has 600 litres of a 12 percent solution of acid. How ma

1.	A manufacturer has 600 litres of a 12 percent solution of acid. How many litres of a 30 percent acid solution must be added to it so that the acid content in the resulting mixture will be more than 15 percent but less than 18 percent?
Answer» 12% solution of acid in 600 l ⇒ 600 × (12/100) = 72 l of acid 15% of 600 l ⇒ 600 × (15/100) = 90 l 18% of 600 l ⇒ 600 × (18/100) = 108 l Let x litres of 18% acid solution be added Given, (600 + x) (15/100) ≥ 72 + (30x/100) (600 + x)15 ≥ 7200 + 30x 9000+ 15x ≥ 7200 + 30x 1800 ≥ 15x x ≤ 120 Let x litres of 18% acid solution be added Given, (600 + x)(18/100) ≤ 72 + (30/100)x (600 + x)18 ≤ 7200 + 30x 10800 + 18 ≤ 7200 + 30x 3600 ≤ 12x x > 300 The solution is 120 ≤ x > 300

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

Answer»

12% solution of acid in 600 l ⇒ 600 × (12/100) = 72 l of acid

15% of 600 l ⇒ 600 × (15/100) = 90 l

18% of 600 l ⇒ 600 × (18/100) = 108 l

Let x litres of 18% acid solution be added

Given, (600 + x) (15/100) ≥ 72 + (30x/100)

(600 + x)15 ≥ 7200 + 30x

9000+ 15x ≥ 7200 + 30x

1800 ≥ 15x

x ≤ 120

Let x litres of 18% acid solution be added

Given, (600 + x)(18/100) ≤ 72 + (30/100)x

(600 + x)18 ≤ 7200 + 30x

10800 + 18 ≤ 7200 + 30x

3600 ≤ 12x

x > 300

The solution is 120 ≤ x > 300