Mixing Iron and Zinc Homework Question

Question

A metal alloy is made by mixing iron and zinc. If 36% of the alloy is zinc and the amount of iron in the alloy is 160 g, calculate the total mass of the alloy.

Answer 1

Zn = Zinc
Fe = Iron
W = weight of alloy (grams)
wZn = weight zinc (grams)
wFe = weight Fe (grams)

36% (zinc)  = 100 *(wZn/W)
160g Fe = wFe
 
W = wZn + wFe

(1) W = wZn + 160g
(2) 36 = 100(wZn/W)  

2 unknowns and 2 equations. Solve for W, the weight of the allow

Simplify

36W = 100(wZn)
wZn = 36W / 100
W = 36W/100 + 160  
100W = 36W + 16000  
64W = 16000
W = (16000/64) = 250g

Verify:
36% Zn, so 64% Fe
.64 (250) = 160 g Fe
.36 (250) = 90 g Zn
Total = 160 + 90 = 250g