A bottle of cordial contains 5litres ,10% is pure fruit juice.how many litres of water must be added to dilute it to 4% fruit juice
Well, well, well. Looks like we've got a juicy question here! So, you want to dilute that cordial down to 4% fruit juice. Let's do some fun math, shall we?
Currently, 10% of the 5-liter bottle is pure fruit juice, which means we have 0.5 liters of fruit juice. To achieve a ratio of 4%, we'll need to have 0.04 times the total volume of juice in fruit juice form.
So, the amount of fruit juice we want in the diluted solution is 0.04 times x liters of juice. And since we're adding water, the total volume of the diluted solution will be 5 liters + x liters.
Now, if we equate the amount of fruit juice we want (0.04x) to the amount of fruit juice we currently have (0.5 liters), we can solve for x:
0.04x = 0.5
Divide both sides by 0.04:
x = 0.5 / 0.04
Now, if we subtract 5 liters (original volume) from x, we'll find out how much water needs to be added:
x - 5 = amount of water
So, let's solve for x and find out the answer to your question!
x = 0.5 / 0.04 = 12.5
Therefore, you'll need to add 12.5 liters of water to dilute that cordial down to 4% fruit juice. Enjoy your less concentrated, but still refreshingly delicious drink!
To solve this problem, we can use the concept of the initial amount of fruit juice in the cordial and the final desired concentration of fruit juice after dilution.
Let's start by finding the initial amount of fruit juice in the cordial. We know that 10% of the 5 liters is pure fruit juice. So, we can calculate it as follows:
Initial amount of fruit juice = 10% of 5 liters
= (10/100) * 5 liters
= 0.1 * 5 liters
= 0.5 liters
Next, we need to determine the amount of fruit juice after dilution at 4% concentration. We'll assume that x liters of water are added to achieve this.
Final amount of fruit juice = 4% of (5 liters + x liters)
= (4/100) * (5 liters + x liters)
= 0.04 * (5 + x) liters
Since we know that the total amount of liquid after dilution is 5 liters (the original amount of cordial), the equation becomes:
(0.04) * (5 + x) liters = 0.5 liters
Now, let's solve for x (the amount of water to be added):
0.04 * (5 + x) liters = 0.5 liters
Multiplying both sides by 100 to remove the decimal:
4 * (5 + x) = 50
Simplifying,
20 + 4x = 50
4x = 50 - 20
4x = 30
Dividing both sides by 4:
x = 30/4
x = 7.5
Therefore, you would need to add 7.5 liters of water to the 5 liters of cordial to dilute it to a 4% fruit juice concentration.
To solve this problem, we can set up a proportion to determine the amount of water needed to dilute the cordial.
Let's start by defining the initial amount of fruit juice in the cordial. We are told that the bottle contains 5 liters and that 10% of it is pure fruit juice.
So, the initial amount of fruit juice in the cordial is 5 liters * (10/100) = 0.5 liters.
Next, let's define the final amount of fruit juice we want to achieve. We are told that we want to dilute the cordial to have a final fruit juice concentration of 4%.
So, the final amount of fruit juice needed is 5 liters * (4/100) = 0.2 liters.
Now, let's subtract the final fruit juice amount from the initial fruit juice amount to find the amount of fruit juice that needs to be diluted.
Amount of fruit juice to be diluted = initial fruit juice amount - final fruit juice amount
= 0.5 liters - 0.2 liters
= 0.3 liters.
Since the fruit juice is diluted by adding water, the amount of water needed is the same as the amount of fruit juice to be diluted, which is 0.3 liters.
Therefore, you need to add 0.3 liters of water to dilute the cordial to a 4% fruit juice concentration.
consider the % of juice before and after adding x liters of water:
.10(5) = .04(5+x)