Answer:
The number of cartons of concentrated orange juice she needs in 4.5 gallons of orange juice is 12 cartons of orange juice
Step-by-step explanation:
The given parameters are;
The volume of the concentrated orange juice = 12 fluid ounce cartons
The ratio of orange juice concentrate to water = 12 fluid ounces to 36 fluid ounces
The amount of orange juice James need = 4.5 gallons = 576 fluid ounces
Therefore;
The ratio of orange juice concentrate to water is 12:36
Therefore;
Let 'x' represent the amount of concentrated orange juice in 4.5 gallons of orange juice, and let 'y' represent the amount of water in the 4.5 gallons of orange juice, we have;
x + y = 4.5 (gallons)...(1)
x:y = 12:36 = 1:3
∴ x/y = 1/3
3·x = y...(2)
From equation (1) and equation (2), we have;
x + y = 4.5
x + 3·x = 4.5
x = 4.5/4 = 1.125
x = 1.125
The amount of concentrated orange juice in 4.5 gallons of orange juice, x = 1.125 gallons
∴ y = 3 × x = 3 × 1.125 = 3.375
y = 3.375
The amount of water in the 4.5 gallons of orange juice, y = 3.375
Therefore, we have;
4.5 gallons = 576 fluid ounces
∴ 1.125 gallons = (576/4.5) × 1.125 = 144 fluid ounces
The amount of fluid ounces per carton = 12 fluidounces/carton
∴ The number of cartons in 144 fluid ounces = 144 fluidounces ÷ 12 fluidounces/carton = 12 cartons
The amount of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 1.125 gallons = 144 fluidounces = 12 cartons
The amount of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 12 cartons of orange juice
The amount (number of cartons) of concentrated orange juice she needs in 4.5 gallons of orange juice, x = 12 cartons of orange juice.
