Answer:
378 children; 150 adults
Explanation:
We can determine the number of children and adults at the pool using a system of equations, where
- C represents the number of children at the pool.
- and A represents the number of adults at the pool.
First equation:
We know that the sum of the number of adults and children at the pool equals the total number of people at the pool:
number of adults + number of children = total number of people
Since there were 528 people at the pool, our first equation is given by:
C + A = 528
Second equation:
We also know that the sum of the revenues earned from the children and adults equals the total revenue:
(admission price * number of children) + (admission price * number of adults) = total revenue.
Since the total revenue was $961.50, our second equation is given by:
1.75C + 2.00A = 961.50
Method to solve: Substitution:
First, we can isolate A in the first equation.
(C + A = 528) - C
A = -C + 528
Solving for C (the number of children):
Now we can solve for C (The number of children) by substituting -C + 528 for A in the second equation (1.75C + 2.00A = 961.50):
1.75C + 2.00(-C + 528) = 961.50
1.75C - 2.00C + 1056 = 961.50
(-0.25C + 1056 = 961.50) - 1056
(-0.25C = -94.5) / -0.25
C = 378
Thus, there were 378 children at the public pool that day.
Solving for A (the number of adults):
Finally, we can solve for A (the number of adults) by plugging in 378 for C in he first equation (C + A = 528):
(378 + A = 528) - 378
A = 150
Thus, there were 150 adults at the public pool that day.