A manufacturer of soft-drinks advertises that their orange soda as "naturally flavored," although it contains only 5% orange juice. A new federal regulation stipulates that to be called "natural" a drink must contain at least 10% fruit juice. How much pure orange juice must this manufacturer add to 900 gallons of orange soda to conform to the new regulation?
amount to be added --- x gallons
.05(900) + 1(x) = .1(900+x)
45 + x = 90 + .1x
.9x = 45
x = 45/.9 = 50
To conform to the new regulation, the orange soda must contain at least 10% fruit juice. Currently, the orange soda contains only 5% orange juice. Let's calculate how much pure orange juice must be added to achieve the required percentage.
1. Convert the percentage to decimal form:
- 10% = 10/100 = 0.10
- 5% = 5/100 = 0.05
2. Set up an equation to determine the amount of pure orange juice needed:
Let x represent the amount of pure orange juice to be added.
(0.05 * 900 gallons) + (x gallons) = 0.10 * (900 + x) gallons
Explanation:
- The current amount of orange juice in 900 gallons of soda is 0.05 * 900 gallons.
- The pure orange juice to be added is x gallons.
- The total amount of orange juice after adding x gallons is (900 + x) gallons.
- To meet the regulation, the total amount of orange juice must be 0.10 times the final volume.
3. Solve the equation for x:
0.05 * 900 + x = 0.10 * (900 + x)
45 + x = 90 + 0.10x (Multiply 0.10 by 900 + x)
x - 0.10x = 90 - 45
0.90x = 45
x = 45 / 0.90
x = 50
Therefore, the manufacturer must add 50 gallons of pure orange juice to the 900 gallons of orange soda to conform to the new regulation.
To determine how much pure orange juice the manufacturer must add to conform to the new regulation, we need to find the difference between the current percentage of orange juice (5%) and the required percentage (10%).
Step 1: Calculate the current amount of orange juice in 900 gallons of soda:
Current amount of orange juice = 5% * 900 gallons
Current amount of orange juice = 0.05 * 900 gallons = 45 gallons
Step 2: Calculate the amount of orange juice needed to reach the required percentage:
Difference in orange juice percentage = 10% - 5%
Difference in orange juice percentage = 0.10 - 0.05 = 0.05
Step 3: Calculate the amount of pure orange juice needed to make up the difference:
Amount of pure orange juice = Difference in orange juice percentage * 900 gallons
Amount of pure orange juice = 0.05 * 900 gallons = 45 gallons
Therefore, the manufacturer needs to add 45 gallons of pure orange juice to the 900 gallons of orange soda to conform to the new regulation.