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: $\displaystyle e$

has: $\displaystyle =$

6 more: $\displaystyle +6$

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

Putting this together into an equation, we have:

$\displaystyle e=2c+6$

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

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

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

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.

Re: Determine an equation

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

Re: Determine an equation

Which variable do you want to be independent?

Re: Determine an equation

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

Re: Determine an equation

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

Re: Determine an equation

I want the variable c to be independent.

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) $\displaystyle e=-c+111$

(2) $\displaystyle e=2c+6$

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.