(PLEASE SOMEONE HELP) James is making orange juice from concentrated frozen orange juice that he must mix with water. The concentrated juice is in 12 fluid ounce cartons. The ratio of orange juice concentrate to water is 12 fluid ounces to 36 fluid ounces. If James needs 4.5 gallons of orange juice, which is 576 fluid ounces, how many cartons of concentrated orange juice does he need?

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.

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step-by-step explanation:

the first option is the answer.