Question 1127524
Adrian, Nathan, and Brian bought lunch from the concession stand. Adrian paid $5.50 for burgers, fries and a drink; Nathan paid $4.00 for a burger and a drink; and Brian paid $4.25 for a burger and fries.
a) write three equations modeling the cost of their lunches using b, f, and d to represent the cost of a burger, fries, and a drink.
b)solve the system of equations to determine the cost of each food item.
i just need help setting it up
<pre>Setup is as follows! The cost of a burger, an order of fries, and a drink cost are: b, f, and d, respectively
We then get: b + f + d = 5.5 ------ eq (i)
             b     + d = 4 -------- eq (ii)
             b + f     = 4.25 ----- eq (iii)
You can easily solve for each variable, since all have 1 as their coefficient. DO not follow that person who advised you to
do a million things and take an awfully long time to solve a SIMPLE, SIMPLE system in 3 equations. He's one of a few who'd make a very 
simple problem EXTREMELY TIME-CONSUMING and COMPLEX. There is ABSOLUTELY no reason for someone to advise a person to do a problem that way. 
Again, DON'T FOLLOW this person unless of course you like to torment yourself!!

b + f + d = 5.5 ------ eq (i)
b     + d = 4 -------- eq (ii)
b + f     = 4.25 ----- eq (iii)
f, or price of an order of fries = {{{highlight_green(matrix(1,3, 5.5 - 4, "=", "$1.50"))}}} ------ Subtracting eq (ii) from eq (i)
Now, LOOK how easy that was!
b + 1.5 = 4.25 ------ Substituting 1.5 for f in eq (iii)
b, or cost of burger = {{{highlight_green(matrix(1,3, 4.25 - 1.5, "=", "$2.75"))}}}
2.75 + 1.50 + d = 5.5 ------- Substituting 1.5 for f, and 2.75 for b in eq (i)
d, or cost of a drink = {{{highlight_green(matrix(1,3, 5.5 - 4.25, "=", "$1.25"))}}}
I went too far. You just wanted the setup but I went all the way! What the heck! 
Maybe my solution will give you some insight into the easiest and most time-consuming way to do the problem.