Answer:
10 pounds of milk chocolate, 15 pounds of dark chocolate, and 10 + 15 = 25 pounds of almond chocolate
Step-by-step explanation:
Let x be the number of pounds of milk chocolate that he needs to use in the mixture. And y is the number of pounds of of dark chocolate. Since the mixture must use almonds chocolate as much as the other 2 combined in term of weight, and the total weight is 50 pounds. That means
milk_choco_weight + dark_choco_weight + almond_choco_weight = 50
x + y + (x + y) = 50
2(x+y) = 50
x+y = 25 or x = 25 - y
Since we know the price of the mixture, we can use the following equation
2.5milk_choco_weight + 4.3dark_choco_weight + 5.5almond_choco_weight = 4.54total_weight
2.5x + 4.3y + 5.5(x+y) = 50*4.54
2.5x + 4.3y + 5.5*25 = 227
2.5x + 4.3y = 227 - 137.5 = 89.5
We can substitute x = 25 - y
2.5(25 - y) + 4.3y = 89.5
62.5 - 2.5y + 4.3y = 89.5
1.8y = 27
y = 15
so x = 25 - y = 25 - 15 = 10
So we need 10 pounds of milk chocolate, 15 pounds of dark chocolate, and 10 + 15 = 25 pounds of almond chocolate
