Answer:
Correct answer: x = 35 grams and y = 65 grams
Step-by-step explanation:
Given:
53% purity of the first alloy
83% purity of the second alloy
x = ? mass of the first alloy
y = ? mass of the second alloy
x + y = 100 grams the mass of the mixture
72.5% purity of the mixture
We can solve the problem by setting up a two system of equations:
First: Second:
53 x + 83 y = 100 · 72.5 x + y = 100
x + y = 100 x : y = (83 - 72.5) : (72.5 - 53)
First system:
y = 100 - x
From the second, we express y as a function of x and replace in the first
and get:
53 x + 83 (100 - x) = 7,250
53 x + 8,300 - 83 x = 7,250
30 x = 1050 ⇒ x = 1050 / 30 = 35 grams
x = 35 grams
y = 100 - 35 = 65 grams
y = 65 grams
Second system:
x + y = 100
x : y = (83 - 72.5) : (72.5 - 53) = 10.5 : 19.5 = 105 : 195 = 7 : 13
x : y = 7 : 13 ⇒ x = (7/13) y
From the second, we express x as a function of y and replace in the first
and get:
(7/13) y + y = 100 / ·(13) ⇒ 7 y + 13 y = 1300 ⇒ 20 y = 1300
y = 1300 / 20 = 65 grams
y = 65 grams
x + 65 = 100 ⇒ x = 100 - 65 = 35 grams
x = 35 grams
God is with you!!!
