Question

A metallurgist has one alloy containing 35 % titanium and another containing 64 % titanium. How many pounds of each alloy must he use to make 52 pounds of a third
alloy containing 38 % titanium? (Round to two decimal places if necessary.)

Answer 1

The pounds of each alloy must he use to make 52 pounds of a third alloy containing 38 % titanium is 5.38 pounds and 46.62 pounds respectively.

Simultaneous equation

Let

• pounds of 35% titanium = x
• Pounds of 64% titanium = y

x + y = 52

0.35x + 0.64y = 0.38(52)

x + y = 52

0.35x + 0.64y = 19.76

From equation (1)

x = 52 - y

• Substitute into equation (2)

0.35x + 0.64y = 19.76

0.35(52 - y) + 0.64y = 19.76

18.2 - 0.35y + 0.64y = 19.76

- 0.35y + 0.64y = 19.76 - 18.20

0.29y = 1.56

y = 1.56/0.29

y = 5.38 pounds

• Substitute y = 5.38 into

x + y = 52

x + 5.38 = 52

x = 52 - 5.38

x = 46.62

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