Write System of Equations from Context

Question

At a particular restaurant, each onion ring has 40 calories and each chicken wing has 75 calories. A combination meal with onion rings and chicken wings has a total of 19 onion rings and chicken wings altogether and contains 970 calories. Write a system of equations that could be used to determine the number of onion rings in the combination meal and the number of chicken wings in the combination meal. Define the variables that you use to write the system.

Answer 1

Let N be the number of onion rings in the combo meal.

Let W be the number of chicken wings in the combo meal.

Then N + W = 19

and

40N + 75W = 970.

The first equation can be written as N = 19 - W, and then substituted for N in the other equation.

40(19-W) +75W = 970

40*19 - 40*W + 75W = 970

760 + 35W = 970

35W = 970 - 760 = 210

W = 210 / 35 = 6

N = 19 - 6 = 19 - 6 = 13

Checking:

N + W = 13 + 6 = 19

40N + 75W = 40*13 + 75*6 = 520 + 450 = 970