Empirical formula tutor

You are given a sample that contains a mixture of the following two arsenic-containing minerals: gersdorffite (NiAsS) and getchellite (AsSbS₃). You start with a sample of this mixture that has a mass of 88.78 grams. You perform a reaction that converts the arsenic (As) in these minerals into the form arsenic(III) oxide (As₂O₃), and 49.54 grams of this product are obtained.

What is the percent by mass of gersdorffite in the original sample? (click here if you want step-by-step help to solve this problem)
Please, give all your calculations with three significant figures.

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Step 1: How many moles of product will be produced from one mole of each of the minerals? For each mole of gersdorffite, moles of arsenic(III) oxide will be produced. For each mole of getchellite, moles of arsenic(III) oxide will be produced.

Step 2: How many grams of product will be produced from one gram of each of the minerals? For each gram of gersdorffite, grams of arsenic(III) oxide will be produced. For each gram of getchellite, grams of arsenic(III) oxide will be produced.

Step 3: Let's construct an algebraic equation that relates the mass of product formed to the mass of the minerals in the sample. Fill the blanks with the appropriate values. Let's define x as the mass of gersdorffite. 49.54 g_As2O3 = x g_NiAsS * g_As2O3/g_NiAsS + (88.78-x) g_AsSbS3 * g_As2O3/g_AsSbS3

Step 5: What is the percent by mass of gersdorffite in the initial sample? % by mass

Composition Determination of a Mixture