Problem
At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain?
Solution
For this case we can set up the following notation
x= number of cheeseburgers
y= small fries
4x +5y= 2310
3x + 2y= 1330
From the first equation we can solve for x and we got:
x= 577.5 - 5/4 y
And now we can replace this into the second equation and we got:
3(577.5 -5/4 y) +2y= 1330
And we can solve for y:
1732.5 - 15/4 y + 2y = 1330
-7/4 y = -402.5
y= 230 cal
And solving now for x we have:
x= 577.5 - 5/4 (230) = 577.5 - 287.5 = 290 cal