Answer:
- cheeseburger: 650 calories
- fries: 500 calories
Step-by-step explanation:
You want to know the numbers of calories in a cheeseburger and an order of fries if 4 cheeseburgers and 3 fry orders have 4100 calories, and 5 cheeseburgers and 6 fry orders have 6250 calories.
Equations
If we let c and f represent the calories in a cheeseburger and an order of fries, respectively, then we can describe the calories in the two orders by ...
- 4c +3f = 4100
- 5c +6f = 6250
Solution
Subtracting the second equation from twice the first gives ...
2(4c +3f) -(5c +6f) = 2(4100) -(6250)
3c = 1950 . . . . . . . simplify
c = 650 . . . . . . . divide by 3
Then the calories in the fries can be found by substituting in the first equation:
4(650) +3f = 4100
3f = 1500 . . . . . . . . . subtract 2600
f = 500 . . . . . . . . divide by 3
There are 650 calories in one cheeseburger, and 500 calories in one order of fries.
__
Additional comment
The attachment shows solution of these equations using the matrix functions of a graphing calculator. It reduces the augmented matrix of coefficients of the equations to a form that makes the variable values apparent.
The method of solution shown above uses the "elimination" technique to eliminate the 'f' variable from the equations. We noticed that the coefficient of 'f' in the second equation was double that in the first equation, so subtracting 2 times the first from the second makes the 'f' coefficient zero. We chose that subtraction so the 'c' coefficient would end up positive.
