A bottle of cordial contains 5litres ,of which 10% I'd pure fruit juice. many liters of water must be added to dilute to 4% fruit juice.can anybody explain please,thanks
If x liters of water are added, then
.10(5) = .04(5+x)
To find the number of liters of water that must be added to dilute the cordial to 4% fruit juice, we need to determine the amount of pure fruit juice in the bottle and then calculate the amount of water needed.
1. Calculate the amount of pure fruit juice in the bottle:
- The bottle contains 5 liters of cordial.
- 10% of the cordial is pure fruit juice.
- To find the amount of pure fruit juice in the bottle, multiply 5 liters by 10% (or 0.10).
- 5 liters * 0.10 = 0.5 liters
2. Calculate the desired amount of pure fruit juice after dilution:
- The desired concentration after dilution is 4%.
- To find the desired amount of pure fruit juice, multiply the total volume of the diluted mixture by the desired concentration.
- Let's assume the total volume of the diluted mixture (cordial + water) is V liters.
- The desired amount of pure fruit juice is V * 4% (or 0.04).
- The equation to represent this is: V * 0.04 = 0.5 liters (from step 1).
3. Calculate the amount of water needed:
- Subtract the amount of pure fruit juice in the bottle (0.5 liters) from the desired amount of pure fruit juice.
- This will give us the amount of water needed to make up the difference.
- 0.5 liters of pure fruit juice / 0.04 = V liters - 0.5 liters of pure fruit juice
- 12.5 liters = V liters - 0.5 liters
- V liters = 13 liters
Therefore, you need to add 13 - 5 = 8 liters of water to dilute the cordial to 4% fruit juice.
To solve this problem, we need to determine how much water needs to be added to reduce the concentration of fruit juice from 10% to 4%.
Step 1: Determine the amount of pure fruit juice in the bottle.
We know that 10% of the 5-liter bottle is pure fruit juice. So, 10% of 5 liters can be calculated as (10/100) * 5 = 0.5 liters.
Step 2: Determine the concentration of fruit juice desired after dilution.
The concentration of fruit juice desired after dilution is 4%.
Step 3: Calculate the amount of liquid after dilution.
Let's assume x liters of water need to be added. After dilution, the total amount of liquid will be 5 liters + x liters.
Step 4: Set up an equation.
The concentration of the fruit juice after dilution can be calculated as (0.5 liters / (5 liters + x liters)) * 100%.
Step 5: Solve the equation.
Set up the equation: (0.5 / (5 + x)) * 100 = 4
Multiply both sides by (5 + x): 0.5 * 100 = 4 * (5 + x)
Simplify: 50 = 20 + 4x
Rearrange the equation: 4x = 50 - 20
Simplify further: 4x = 30
Step 6: Calculate the amount of water needed.
Divide both sides by 4: x = 30 / 4
Simplify: x = 7.5
Based on the calculations, 7.5 liters of water must be added to dilute the cordial to a 4% fruit juice concentration.