This is another system of equations problem.
I will use x to represent children and y to represent the adults.
So the two equations you're going to have are:
2.5x + 5.5y = 7734
x + y = 2220.
It's best to use the substitution method here.
Let's take x + y = 2220. Solve for x by subtracting y on both sides.
The equation for x is now x = 2220 - y.
Substitute this into the other equation.
2.5(2220-y) + 5.5y = 7734.
Solve regularly from here.
5550 - 2.5y + 5.5y = 7734.
Combine like terms then divide.
3y = 2184.
y = 728.
Now that you know y, solve for x.
2220 - 728 = x.
x = 1492.
We both know x and y but let's check our answer by plugging the numerical values of both x and y into the equations.
2.5(1492) + 5.5(728) = $7734.
Multiply the numbers.
3730 + 4004 = 7734.
By adding both numbers you'll get 7734 = 7734. So the x and y values are correct.
