How many liters of a 40% sugar solution must be mixed with 30 liters of a 60% sugar solution to make a 56 % sugar solution?

7.5 liters

Step-by-step explanation:

Here what we need to know is the liters of the first solution, that we will call x. We know that the 40% of x plus the 60% of 30 MUST be equal to the 56% of total liters. The total liters are the sum of both substances, i. e, the x liters of the 1st sugar solution and the 30 liters of the second, which is 30+x liters. So, we have that:

0.4*x + 0.6*30 = 0.56 (30+x)

Using distributive and the fact that 0.6*30 = 18 and 0.56*30=16.8

0.4x + 18 = 16.8 + 0.56x

Subtract 16.8 in both sides:

0.4x + 18 - 16.8 = 0.56x

0.4x + 1.2 = 0.56 x

Subtract now 0.4x in both sides:

1.2 = 0.56 x - 0.4x

1.2 = 0.16x

Divide both sides by 0.16

1.2/0.16 = 0.16/0.16 x

7.5 = x

So, the first solution must be of 7.5 liters in order to have a 56% in the mixture.