How much of each alloy should be mixed to attain the 100 grams of alloy with 16​% ​titanium?

Question

A metallurgist has an alloy with 10% titanium and an alloy with 20% titanium. He needs 100 grams of an alloy with 16% titanium. How much of each alloy should be mixed to attain the 100 grams of alloy with 16% titanium?

Answer 1

To answer a question like this, you need to multiply the concentration by the amount of each material you are starting with.  Add those together and you will get the product of the concentration and amount of the final mixture.

 

Let's say we have x of 10% and y of 20%.

 

.10x + .20y = .16(100)

x + y = 100

 

y = 100 - x

.10(x) + .20(100 - x) = .16(100)

.1x + 20 - .2x = 16

-.1x + 20 = 16

-.1x = -4

x = 40

y = 100 - 40 = 60

 

So use 40 grams of 10% and 60 grams of 20%.