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.

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+5 votes

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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

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