# Math Help - A simple explanation to a question

1. ## 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 cartridges sold at per cartridge, (since is the number of cartridges sold, in thousands) and . Substituting into the equation yields

.

Solving this equation for yields

.
Since is a constant, the function can be written as . To determine how many cartridges will be sold at per cartridge, you need to evaluate . Since is given in thousands, there will be cartridges sold at 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.

2. ## 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.

3. ## 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?

4. ## Re: A simple explanation to a question

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

Multiply both sides by 20+a:

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

Then divide both sides by 100:

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

5. ## 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 $100 = \dfrac{3000}{2(10)+a}$ ?

6. ## 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.