# Math Help - Determine an equation

1. ## Determine an equation

Hey guys,

If you drink a cola and an energy drink, you consume 111 mg of caffeine. The energy drink has 6 more than twice the number of mg of caffeine as compared to the cola.
Use a system of equations and a graph to determine how many milligrams of caffeine are in an energy drink and a cola. Verify your answer.

Lets say c = cola and e = energy

Equation: c + e = 111 and c + 2e + 6 = 111

Are the equations right? How can get the task done?

2. ## Re: Determine an equation

Your first equation is correct, but the second is not. Let's look at the statement:

The energy drink has 6 more than twice the number of mg of caffeine as compared to the cola.

The energy drink: $e$

has: $=$

6 more: $+6$

than twice the number of mg of caffeine as compared to the cola: $2c$

Putting this together into an equation, we have:

$e=2c+6$

Now, substitute this into the first equation for $e$ to get:

$c+(2c+6)=111$

Solve this for $c$, then use the equation $e=2c+6$ to find $e$.

3. ## Re: Determine an equation

Hey ford2008.

The idea you have is correct but in your second equation having 6 more than twice the number means that e = 6 + 2c or c = 6 + 2e (it doesn't matter which one you choose). This would make the second equation c + 2c + 6 = 111 or 3c + 6 = 111.

4. ## Re: Determine an equation

Does anyone know how to make a graph out of these 2 equations?

5. ## Re: Determine an equation

Which variable do you want to be independent?

6. ## Re: Determine an equation

the variable c+e=111 should be the independent.

7. ## Re: Determine an equation

I mean which variable c or e do you want to be independent, that is will represent the horizontal axis?

8. ## Re: Determine an equation

I want the variable c to be independent.

9. ## Re: Determine an equation

When I graph linear equations, I find the easiest way is to write the equations in slope-intercept form. For your system, this would be:

(1) $e=-c+111$

(2) $e=2c+6$

To graph (1), we now simply plot the point (0,111) then move 1 unit to the right and 1 unit down to the point (1,110) and plot this. Now draw the line that contains these two points.

To graph (2), plot the point (0,6). then move 1 unit to the right and 2 units up to the point (1,8) and plot this. Then draw the line containing these two points.