Let's begin by assuming we are trying to find a weight percent and that volumes are additive (they should be for SAT math).
With 45 grams of sugar and 55 grams of water, the new total mass will be 45 + 55 = 100 grams of mixture. This mixture is what's referred to as the 'sugar syrup'.
Formula for weight percent:
weight percent of Component A = [ (mass of component of Component A) / (total mass of mixture) ] *100
You can use this formula for any component in your mixture, even if you have more than 2 components. The weight percent of all the components added together must equal 100%.
Using this formula, we can plug in the mass of sugar and the total mass of the sugar syrup.
weight percent of sugar = [ 45 grams / 100 grams ] * 100 = 45%
Note that your mass units do have to be the same so they cancel out.
