Question

How much pure maple syrup should be added to 48 tablespoons of a 45% solution in order to obtain a 60% solution?

Answer 1

Let x = number of tbsp of pure maple syrup 1.00x = maple syrup content of pure syrup0.45(48) = maple syrup content of 45% solution0.60(x+48) = maple syrup content of mixtureThen, 1.00x + 0.45(48) = 0.60(x+48)
x + 21.6 = 0.60x + 28.80.40x = 7.2x = 18 tbsp

Answer 2

You can use the figures given to find out how many tablespoons are to be added to the solution to get the needed solution.

The amount of pure maple syrup that has to be added to the given solution to make it 60% solution is 18 tablespoons.

How to find how many tablespoon of pure syrup is to be added to make the given solution 60%?

We will measure the amounts in given tablespoon unit only. This will help us get to the solution easily without any additional conversion.

The solution we've taken is 48 tablespoon.

It is 45% solution which means that 45% of the total solution is made up of pure syrup.

We need the solution to be 60%

The amount of syrup we have in the given solution is

$A_{syrup} = \dfrac{A_{sol}\times 45}{100} = \dfrac{48 \times 45}{100} = 21.6 \: \rm tablespoons$

Let we add x tablespoons of pure syrup, then the resultant solution will have the amount of syrup in it as:

$\dfrac{(\text{current amount of syrup + c}) \times 100}{\text{current amount of solution + c}} = 60\%\\\\\dfrac{(A_{syrup} + c)\times 100}{A_{sol} + c} = 60\%\\\\60A_{sol} + 60c = 100A_{syrup} + 100c\\\\60 \times 48 - 100 \times 21.6 = 40c\\\\c = \dfrac{720}{40} = 18 \: \rm tablespoons$

Thus,

The amount of pure maple syrup that has to be added to the given solution to make it 60% solution is 18 tablespoons.

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