Problema Solution
One alloy contains 80 percent gold (by weight) and another alloy contains 55 percent gold. How many grams of each alloy should be combined to make 40g of an alloy that contains 70 percent of gold?
Answer provided by our tutors
Let
x = the weight of the first alloy that contains 80% gold, that is 0.80*x g gold
y = the weight of the second alloy that contains 55% gold, that is 0.55*y g gold
and
x + y = 40 (total weight of the new alloy is 40)
(0.80*x + 0.55*y)/(x+y) = 0.70 (the new alloy have 70% gold)
By solving the system equations
x + y = 40
(0.80*x + 0.55*y)/(x+y) = 0.70
we find
x = 24g
y = 16g
We need to combine 24g of the first alloy and 16 grams of the second to get 40g alloy that has 70% gold.