How many litres of water will have to be added to 1125 litres of the 45% solution of acid so - Maths - Linear Inequalities

Question

How many litres of water will have to be added to 1125 litres of
the 45% solution of acid so that the resulting mixture will contain
more than 25% but less than 30% acid content?

Gopal Mohanty · Accepted Answer

Let x litres of water is required to be added.

Then, total mixture = (x + 1125) litres

It is evident that the amount of acid contained in the resulting mixture is 45% of 1125 litres.

This resulting mixture will contain more than 25% but less than 30% acid content.

∴30% of (1125 + x) > 45% of 1125

And, 25% of (1125 + x) < 45% of 1125

30% of (1125 + x) > 45% of 1125

25% of (1125 + x) < 45% of 1125

∴562.5 < x < 900

Thus, the required number of litres of water that is to be added will have to be more than 562.5 but less than 900.

25% of (1125 + x) < 45% of 1125

∴562 5 < x < 900 Thus, the required number of litres of water that is to be added will have to be more than 562 5 but less than 900

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?