Question

A metallurgist has one alloy containing 35% titanium and another containing 52% titanium. How many pounds of each alloy must be use to make 45 pounds of a third alloy containing 47% titanium

Answer 1

Explanation:

% in calculations are always represented as hundredths, as 100% represents the whole, and n% = n/100 of the whole.

x = pounds of 35% alloy.

y = pounds of 52% alloy.

x + y = 45

0.35x + 0.52y = 0.47(x + y)

from the first equation we get e.g.

x = 45 - y

now we use this in the second equation :

0.35(45 - y) + 0.52y = 0.47((45 - y) + y)

15.75 - 0.35y + 0.52y = 0.47(45 - y + y)

15.75 + 0.17y = 0.47×45 = 21.15

0.17y = 5.4

y = 5.4/0.17 = 31.76470588... pound

x = 45 - y = 13.23529412... pound

he needs to use

31.76470588... pounds of the 52% alloy

13.23529412... pounds of the 35% alloy.