Question

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?

Answer 1

7.5 liters

Explanation:

We need to make an equation.

40%, x liters

60%, 30 liters

=56%

0.40(x) + 0.60 (30) = 0.56 (x + 30)

0.40x + 18 = 0.56x + 16.8

18 - 16.8 = 0.56x - 0.40x

1.2 = 0.16x

7.5 = x

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Answer 2

7.5 liters of a 40% sugar solution

Explanation:

Let

x ----> liters of a 40% sugar solution

Remember that

`40\%=40/100=0.40\\60\%=60/100=0.60\\56\%=56/100=0.56`

we know that

The amount of liters of a 40% sugar solution (x) multiplied by 0.40 plus the amount of liters of a 60% sugar solution (30 L) multiplied by 0.60 must be equal to the total amount of liters mixed (x+30) multiplied by 0.56

`0.40x+0.60(30)=0.56(x+30)`

solve for x

`0.40x+18=0.56x+16.8\\0.56x-0.40x=18-16.8\\0.16x=1.2\\x=7.5\ L`