Answer: milk chocolate = 10 pounds
Dark chocolate =15 pounds
Dark chocolate with almonds = 25 pounds.
Step-by-step explanation:
What we have here is a proportion problem.
Milk chocolate = $2.90
Dark chocolate = $4.90
Dark chocolate with almonds = $5.50
We are to have 50 pounds of mixed chocolate
Amount the grocer makes from this
= $4.80 × 50 = $240
However, we must consider how much the grocer would have made if he had sold them separately
Weight of milk chocolate = x
Weight of dark chocolate = y
Weight of dark chocolate with almond = z
x+y = z (according to the question)
x+y+z= 50
Equating the collective amount of each type of chocolate with the amount they all cost together
2.90x + 4.90y + 5.50z = 50(4.80)
2.90x + 4.90y + 5.50z = $240
But z = x + y
2.90x + 4.90y + 5.50 (x+y) = $240
2.90x + 4.90y + 5.50x + 5.50y = 240
8.40x + 10.40y = 240 .....eqn 1
Since x + y + z = 50
x + y = 50 - z
But x+ y = z
x + y = 50 - (x+y)
x + y = 50 - x - y
2x + 2y = 50
(Divide through by 2)
x+y = 25 ...... Eqn 2
y = 25 - x
Substitute for y in eqn2
8.4x + 10.4 (25-x) = 240
8.4x + 260 - 10.4x = 240
8.4x - 10.4x = 240 - 260
-2x = -20
x = 10 pounds
y = 25-x
y = 25-10
y=15pounds
x+y+z= 50
10+15+z= 50
25+z=50
z= 50-25
z = 25
