Answer: 15 pounds of milk chocolate, 10 pounds of dark chocolate and 25 pounds of dark chocolate with almonds is needed in the mixture.
Step-by-step explanation:
Let x represent the number of pounds of milk chocolate that would be in the mixture.
Let y represent the number of pounds of dark chocolate that would be in the mixture.
Let z represent the number of pounds of dark chocolate with almonds that would be in the mixture.
Since the mixture would be 50 pounds, it means that
x + y + z = 50- - - - - - - - - - - 1
He wants to make a mixture of 50 pounds of mixed chocolates to sell at $4.61 per pound. The total cost of the mixture would be 50 × 4.61 = $230.5. Milk chocolate would sell at $2.60 per pound, dark chocolate at $4.40 per pound, and dark chocolate with almonds at $5.90 per pound. It means that
2.6x + 4.4y + 5.9z = 230.5- - - - - - -2
The mixture is to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined. It means that
z = x + y
Substituting z = x + y into equation 1 and equation 2, it becomes
x + y + x + y = 50
2x + 2y = 50
Dividing both sides by 2, it becomes
x + y = 25
x = 25 - y- - - - - - - - - 3
2.6x + 4.4y + 5.9(x + y) = 230.5
2.6x + 4.4y + 5.9x + 5.9y = 230.5
2.6x + 5.9x + 4.4y + 5.9y = 230.5
8.5x + 10.3y = 230.5- - - - - - - - - 4
Substituting equation 3 into equation 4, it becomes
8.5(25 - y) + 10.3y = 230.5
212.5 - 8.5y + 10.3y = 230.5
- 8.5y + 10.3y = 230.5 - 212.5
1.8y = 18
y = 18/1.8
y = 10
x = 25 - y = 25 - 10
x = 15
Substituting x = 15 and y = 10 into z = x + y,
z = 15 + 10 = 25
