A simple explanation to a question

Sorry for all the post, but I don't have access to a tutor to blow past this stuff quickly..

When they say 100 = 3000/2(10)+a, they "magically" change it to 100(20+a)=3000 to make it easier to solve. How do they know they can do this?

For http://sat.collegeboard.org/mathmlge...athMCq3_13.png cartridges sold at http://sat.collegeboard.org/mathmlge...athMCq3_14.png per cartridge, http://sat.collegeboard.org/mathmlge...athMCq3_15.png (since http://sat.collegeboard.org/mathmlge...athMCq3_16.png is the number of cartridges sold, **in thousands) and http://sat.collegeboard.org/mathmlge...athMCq3_17.png. Substituting into the equation yields**

http://sat.collegeboard.org/mathmlge...athMCq3_18.png.

**Solving this equation for http://sat.collegeboard.org/mathmlge...athMCq3_19.png yields**

**http://sat.collegeboard.org/mathmlge...athMCq3_20.png**

** http://sat.collegeboard.org/mathmlge...athMCq3_21.png**

** http://sat.collegeboard.org/mathmlge...athMCq3_22.png.**

**Since http://sat.collegeboard.org/mathmlge...athMCq3_23.png is a constant, the function can be written as http://sat.collegeboard.org/mathmlge...athMCq3_24.png. To determine how many cartridges will be sold at http://sat.collegeboard.org/mathmlge...athMCq3_25.png per cartridge, you need to evaluate http://sat.collegeboard.org/mathmlge...athMCq3_26.png. Since http://sat.collegeboard.org/mathmlge...athMCq3_27.png is given in thousands, there will be http://sat.collegeboard.org/mathmlge...athMCq3_28.pngcartridges sold at http://sat.collegeboard.org/mathmlge...athMCq3_29.png per cartridge.**

When they say 100 = 3000/2(10)+a, they "magically" change it to 100(20+a)=3000 to make it easier to solve. How do they know they can do this?

How the heck did they turn 100 into 20 and 3000 into 300? How did they know to do that?

We'll start there.. I know this is very simple, but I learn awfully on the computer & when I have too much time to confuse myself because I can't ask right away. Lol.. Keep that in mind when explaining. (Worried)

Re: A simple explanation to a question

Multiply both sides of the equation by 20+a. On the right hand side, you will be both multiplying 3000 by 20+a and dividing by 20+a, so essentially, you are multiplying 3000 by 1.

The next step, they divide both sides by 100. 100*(20+a) divided by 100 is 20+a. 3000 divided by 100 is 30.

Re: A simple explanation to a question

I'm confused. What? Which part do you multiply 20+a on both sides? How would 20+a eventually turn into 3000 x 1?

Re: A simple explanation to a question

$\displaystyle 100 = \dfrac{3000}{2(10)+a}$

Multiply both sides by 20+a:

$\displaystyle 100(20+a) = \dfrac{3000}{20+a}(20+a) = 3000$

Then divide both sides by 100:

$\displaystyle \dfrac{100(20+a)}{100} = 20+a$ on the LHS and $\displaystyle \dfrac{3000}{100} = 30$ on the RHS.

Re: A simple explanation to a question

Alright, that made a bit more sense. But question.. How do you know to multiply both sides by 20+a, upon seeing http://latex.codecogs.com/png.latex?...3000}{2(10)+a} ?

Re: A simple explanation to a question

I want to remove fractions. I do that by multiplying both sides of the equation by the denominator of a fraction.