This week in Pre-Calc 11 we learned about Applications of Radical Equations, which is essentially applying the skills we have learned related to Radical Equations, to real life situations.

The basic concepts and skills you must apply in order to do these questions are,

1. Read problems and understand what is being asked.

2. Introduce a variable to represent an unknown number.

3. Write an equation using the given info.

4. Solving.

5. Check your answer to make sure it makes sense.

There are four main types of problems we look at,

1. Distance, Speed, and Time Problems.

2. Motion Problems.

3. Work Problems.

4. Proportion Problems.

For this example I will do a proportion problem.

Example: How much Kool Aid powder must be added to 4L of water to make a solution containing 35% Kool Aid?

By applying logic and basic math skills we can come up with a formula using the clues given to us in this problem.

Proportion problems follow the basic ratio of \frac {part}{total}

Knowing this we can determine the first part of our equation, \frac {35}{100}

We can also determine the second part by using this idea of part / total. Part of the solution would be the amount of Kool Aid powder, which is what we are trying to find, or “x”. The total would be the amount of Kool Aid plus the 4L of water.

So that means our full equation is \frac {35}{100} = \frac {x}{x+4}

Then we can use our skills with Rational Equations and cross multiply to find x.

35x +140 = 100x

 

140 = 65x

 

x = 2.15

 

You would need to add about 2.15L of Kool Aid to the 4L of water to have a solution with 35% Kool Aid.