Saline solution A is 10% strength and saline solution B is 5% strength. I have an order for 6 litres of an 8% saline solution. To fill the order how many litres of solution A should be diluted with solution B? (Hint. Assume a 1% solution contains r grams of salt per litre.)

Let x = volume of saline solution A,

y = volume of saline solution B.

We're going to set up two equations.

Firstly, x + y = 6. That gives us y = 6 - x (1)

Second, 0.1x + 0.05y = 0.08•6,

or 0.1x + 0.05y = 0.48 (2)

Substitute (1) into (2):

0.1x + 0.05 (6 - x) = 0.48

0.1x + 0.3 - 0.05x = 0.48

0.05x + 0.3 = 0.48

Subtract 0.3 from both sides:

0.05x = 0.18

x = 3.6

Then y = 6 - 3.6 = 2.4

So we have to use 3.6 litres of solution A and 2.4 litres of solution B.

18/5 (or 3.6) liters of solution A should be diluted with solution B.