Amixture of potassium bromide and potassium hydroxide has a total mass of 5.50 g. if the mixture contains 2.45 g k, what is the mass in grams of potassium hydroxide in the mixture?

KBr molar mass = 39 + 80 = 119 grams which has x moles in the mixture
KOH molar mass = 39 + 17 = 56 grams which has y moles in the mixture

119x + 56 y = 5.50
39*x + 39*y = 2.45 that's because 

Every mole of KOH and KBr has exactly 1 mole of K in each molecule.

I won't go through the math, but the answer is
x = 0.0315
y = 0.0314
The answer to your question involves y*56 from which we get 1.758 grams Sodium Hydroxide

To check we
119x + 56y = 5.50 grams of mixture.
119* 0.0315 = 3.75 grams
56 * 0.0324 = 1.758
Total = 5.51 which is about as close as you can get when rounding.