# Determine an equation

• Oct 28th 2012, 08:29 PM
ford2008
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?
• Oct 28th 2012, 08:43 PM
MarkFL
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\$.
• Oct 28th 2012, 08:46 PM
chiro
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.
• Oct 29th 2012, 06:06 PM
ford2008
Re: Determine an equation
Does anyone know how to make a graph out of these 2 equations?
• Oct 29th 2012, 06:27 PM
MarkFL
Re: Determine an equation
Which variable do you want to be independent?
• Oct 30th 2012, 06:28 PM
ford2008
Re: Determine an equation
the variable c+e=111 should be the independent.
• Oct 30th 2012, 06:54 PM
MarkFL
Re: Determine an equation
I mean which variable c or e do you want to be independent, that is will represent the horizontal axis?
• Oct 30th 2012, 07:43 PM
ford2008
Re: Determine an equation
I want the variable c to be independent.
• Oct 30th 2012, 07:55 PM
MarkFL
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.