Question

a metallurgist has an alloy with 15% 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 71% titanium?

Answer 1

this problem is weird. do you have the answer?
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i came up with an answer but it assumed that there is the same amount of both alloys

Answer 2

yeah the answer came out to be 60 grams of the alloy with 10% of titanium needed and 40 grams of the alloy with 25% of titanium are needed. I don't know how that was the answer...

Answer 3

sorry for being so late and for calling it weird. its actually fine. here is how to solve it:

let x = grams of alloy A and y = grams of alloy B.

now i just noticed you gave 2 sets of A and B. in the initial problem its 15% and 20% and just above its 10% and 25%

for the initial assumption we have:

x + y = 100
which is
mass of A + mass of B = 100

and

0.15x + 0.20y = 0.17*100
which is
fractionA*massA + fractionB*massB = fractionTotal*massTotal

the first equation can be rearranged to x = 100 - y and we can plug that into the second equation to reduce it to a 1 variable equation:

0.15(100 - y) + 0.20y = 17
15 - 0.15y + 0.20y = 17
0.05y = 2
y = 40 grams
x = 100 - y = 60 grams