Thread: Determine an equation

Hey guys,

the task:
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?

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:

has:

6 more:

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

Putting this together into an equation, we have:



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



Solve this for , then use the equation to find .

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.

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

Which variable do you want to be independent?

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

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

I want the variable c to be independent.

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)

(2)

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.