Answer:
Part A:
(0.20)(10) = (0.05)(x) + (0.40)(10 - x)
Part B:
5.7 litres of 5% and 4.3 litres of 40%
Explanation:
Let's assume she will stick with 10 litres in total for her mixture. (Maybe that's the size of her container.)
Let the volume of 5% by x litres.
Therefore the volume of 40% will equal 10 - x.
Reason: 10 litres total, if we use 2 litres of the one, we'll use 8 litres of the other. Get it?
Moving along...
So:
(0.20)(10) = (0.05)(x) + (0.40)(10 - x)
Now we solve the equation...
2 = 0.05x + 4 - 0.4x
2 - 4 = - 0.35x
-2 = -0.35x
let's multiply both sides by 100 to get rid of the decimal
-200 = -35x
x = 200/35
x = 5.7 litres (volume of 5% solution needed)
volume of 40% = 10 - 5.7 = 4.3 litres