A litre of orange cordial contains 10% orange juice. How many miillilitres of orange juice must be added to produce a mixture containing 50% orange juice? Could you please explain step by step and explain why the answer won't be 400?
the 10% mix has 900 ml of water
So, you will need 900 ml of juice at the end to make it 50%
so, add 800ml of juice
adding 400ml only gives you 500ml of juice in 1400ml of mix, for 5/14 = 35.7% juice
I have the same question Reiny, but how would it be (1000 + x), since the question is mentioning about half a litre, which is 500ml
Well, because the answer is 800 ml
.1(1000) + x = .5(1000+x)
100 + x = 500 + .5x
.5x = 400
x = 800
To solve this problem, we can use a simple equation:
Let's say we need to add x millilitres of orange juice.
The initial amount of orange juice in the cordial is 10% of 1 litre, which is (10/100) * 1000 ml = 100 ml.
After adding x millilitres of orange juice, the total volume of the mixture will be (1000 + x) millilitres, and the amount of orange juice in it will be 100 ml + x ml.
The desired concentration of orange juice in the mixture is 50%.
So, we can set up the equation:
(100 ml + x ml) / (1000 ml + x ml) = 50/100
Simplifying this equation, we get:
(100 + x)/(1000 + x) = 1/2
Now, let's solve this equation step by step:
1. Cross-multiply:
2 * (100 + x) = (1000 + x)
2. Expand:
200 + 2x = 1000 + x
3. Combine like terms:
2x - x = 1000 - 200
x = 800
So, we need to add 800 millilitres of orange juice to produce a mixture containing 50% orange juice.
Now let's explain why the answer is not 400:
If you were to add 400 millilitres of orange juice, the equation would look like this:
(100 + 400) / (1000 + 400) = 50/100
Simplifying:
500 / 1400 = 1/2
This equation does not hold true, as the left side is not equal to the right side. Therefore, 400 millilitres of orange juice would not give us a mixture containing 50% orange juice. The correct amount is 800 millilitres.