Answer:
Using a system of equations, however, allows me to use two different variables for the two different unknowns.
number of adults: a
number of children: c
With these variables, I can create equations for the totals they've given me:
total number: a + c = 2200
total income: 4a + 1.5c = 5050
Now I can solve the system for the number of adults and the number of children. I will solve the first equation for one of the variables, and then substitute the result into the other equation:
a = 2200 – c
4(2200 – c) + 1.5c = 5050
8800 – 4c + 1.5c = 5050
8800 – 2.5c = 5050
–2.5c = –3750
c = 1500
Now I can back-solve for the value of the other variable:
a = 2200 – (1500) = 700
I have values for my two variables. I can look back at my definitions for the variables to interpret these values. To answer the original question, there were:
1500 children and 700 adults.
