Problema Solution
A metallurgist has one alloy containing 39% copper and another containing 57% copper. How many pounds of each alloy must he use to make 47 pounds of a third alloy containing 56% copper?
Answer provided by our tutors
let
x = the pounds of the alloy containing 39% copper
y = the pounds of the alloy containing 57% copper
using x an y he will make 47 pounds of a third alloy containing 56% copper, that is why
x + y = 47
the wight of the copper in x (39% of x) + the weight of the copper in y (57% of y) = the weight of the copper in the new alloy (56% of 47)
0.39*x + 0.57*y = 0.56*47
by solving the system of equations
x + y = 47
0.39*x + 0.57*y = 0.56*47
we find
x = 2.61 lbs
y = 44.39 lbs
he must use 2.61 lbs of the alloy containing 39% copper and 44.39 lbs alloy containing 57% copper.