Introduction:

In some food processing and laboratory applications, it is necessary to mix two solutions of different concentrations to achieve a specific concentration in the final mixture. This article explains how to calculate the amounts of two sucrose solutions with different concentrations to prepare 1 kg of a 50g/100g sugar syrup.

Given Information:

• Solution A: 30g of sucrose/100g of solution

• Solution B: 60g of sucrose/100g of solution

• Desired syrup concentration: 50g of sucrose/100g of syrup

• Total weight of the final syrup: 1 kg (1000g)

Step 1: Define Variables

Let:

• x = the amount (in grams) of Solution A to be mixed

• y = the amount (in grams) of Solution B to be mixed

We know:

• x + y = 1000g (because the total weight of the syrup is 1 kg)

Step 2: Set Up the Equation for Sugar Concentration

We also know the sugar content in the solutions:

• Solution A has 30g of sugar per 100g, so in x grams of Solution A, the sugar content is 30100×x=0.30x\frac{30}{100} \times x = 0.30x10030​×x=0.30x grams.

• Solution B has 60g of sugar per 100g, so in y grams of Solution B, the sugar content is 60100×y=0.60y\frac{60}{100} \times y = 0.60y10060​×y=0.60y grams.

For the final syrup to have a 50g/100g sugar concentration, the total sugar in the final mixture must be 50% of 1000g:

• Total sugar in the final mixture = $50\%\times 1000g=500g$.

So, the sugar from both solutions must add up to 500g:

$$0.30x+0.60y=500$$

Step 3: Solve the System of Equations

We now have the following system of equations:

1. $x+y=1000$

2. $0.30x+0.60y=500$

Solve for y in terms of x from the first equation:

$$y=1000-x$$

Substitute into the second equation:

$$0.30x+0.60(1000-x)=500$$ $$0.30x+600-0.60x=500$$ $$-0.30x+600=500$$ $$-0.30x=500-600$$ $$-0.30x=-100$$ x=−100−0.30=333.33gx = \frac{-100}{-0.30} = 333.33gx=−0.30−100​=333.33g

So, x ≈ 333g of Solution A.

Find y:

$$y=1000-333=667g$$

So, y ≈ 667g of Solution B.

Conclusion:

To prepare 1 kg of a 50g/100g sugar syrup, you need to mix 333g of Solution A with 667g of Solution B.

Answer: 1. 333 g A + 667 g B.