Answer:
Let's start by using the formula for mixing two solutions to set up an equation. The formula is:
(concentration of solution 1) x (volume of solution 1) + (concentration of solution 2) x (volume of solution 2) = (concentration of resulting solution) x (total volume of resulting solution)
In this problem, solution 1 is the 25% sugar syrup, solution 2 is the 10% sugar syrup, and the resulting solution is 15% sugar syrup. We are also given that the total volume of the resulting solution is 120 grams. Let's use x to represent the volume of the 10% sugar syrup that is mixed with the 25% sugar syrup. Then we can write:
(0.25)(120-x) + (0.10)(x) = (0.15)(120)
Simplifying this equation, we get:
30 - 0.25x + 0.10x = 18
0.15x = 12
x = 80
Therefore, we need to mix 80 grams of the 10% sugar syrup with 40 grams of the 25% sugar syrup to get 120 grams of 15% sugar syrup.
To find the amount of pure sugar in the 120 grams of 15% syrup, we can use the fact that the concentration of pure sugar in the resulting solution is 15%. That means that 15% of the 120 grams is pure sugar. We can find this by multiplying 120 by 0.15:
120 x 0.15 = 18
So there are 18 grams of pure sugar in the 120 grams of 15% syrup.