Question

a metallurgist has an alloy with 10% titanium and an alloy with 20% titanium. he needs 100 grams of an alloy with 17% titanium. how much of each alloy should be mixed to attain the 100 grams of alloy with 17% titanium?

Answer 1

Let us say that:

x = mass of 10% titanium alloy required

y = mass of 20% titanium alloy required

To solve this problem, we set-up two mass balances or equations.

Overall mass balance: x + y = 100

x = 100 – y ---> 1

Titanium mass balance: 0.10 x + 0.20 y = 0.17 (100)

0.10 x + 0.20 y = 17 ---> 2

Now we combine equations 1 and 2:

0.10 (100 – y) + 0.20 y = 17

10 – 0.10 y + 0.20 y = 17

0.10 y = 7

y = 70 g

Calculating for x using equation 1:

x = 100 – y

x = 100 – 70

x = 30 g

Answer:

x = 30 g of 10% titanium alloy required

y = 70 g of 20% titanium alloy required