Concentrations Confusion

Baldini wrote:Hi,
I'm trying to brush up on my "concentration/ mixture" type questions and have come across a problem which I can not solve. It relates to two similar questions:

1. One gallon of soft drink is made of 40% orange juice and 60% water, how many additional gallons of orange juice must be mixed in to make the orange juice 60% of the soft drink?

2. How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution.

The solution to the first, as an algebraic expression, is the following:
(0.4 + x)/(1 + x) = 0.6 ;

whilst the solution to the second is the following:
0.15/(1 + x) = 0.1

Can someone please explain why the formulas are not the same; more specifically, why is the 2nd formula not (0.15 + x)/(1+x) = 0.1?

Many thanks in advance for all contributions,

First lets find how the two questions are similar.
The first asks how much orange juice needs to be added to increase the concentration of orange juice.
The second asks how much Water needs to be added to a Salt solution to Decrease the salinity of the mixture.

If you want to set up the questions to look the same I would ask the second one like this
How much water needs to be added to a 85% salt water solution to increase the amount of water to be 90%.

If you ask it this way then the structure of the equations you use to solve should be the same.[/u]

Baldini wrote:Hi,
I'm trying to brush up on my "concentration/ mixture" type questions and have come across a problem which I can not solve. It relates to two similar questions:

1. One gallon of soft drink is made of 40% orange juice and 60% water, how many additional gallons of orange juice must be mixed in to make the orange juice 60% of the soft drink?

2. How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution.

The solution to the first, as an algebraic expression, is the following:
(0.4 + x)/(1 + x) = 0.6 ;

whilst the solution to the second is the following:
0.15/(1 + x) = 0.1

Can someone please explain why the formulas are not the same; more specifically, why is the 2nd formula not (0.15 + x)/(1+x) = 0.1?

Many thanks in advance for all contributions,

There is no formula used here.. or at least I don't see any formula being used.. except just a logical percentage equation..

1. Let's say 0.4g orange juice and 0.6g water are present and you add x gallons orange juice. So the percentage of orange juice after you add this x gallons of orange juice to the whole mixture would be
Total orange juice present/Total volume of juice

Total orange juice now is 0.4 + x
and total juice is 0.4 + 0.6 + x = 1 + x

=> (0.4 + x)/(1 + x) = 0.6 As you see, this is no formula but just a logical percentage equation.. that's it..

2. The above is the same logic used in this 2nd question too..

0.15 = salt present
1 = total volume of salt and water
x = water added.. and here we need to equate this to percentage of salt after water is added.. that percentage is 10% because that's what is given to us in the question.

so it just becomes.. 0.15/(1 + x) = 0.1

I couldn't think of a simpler way to explain this.. HTH