Answer:
There were 63 adults and 235 children at the public swimming pool.
Explanation:
We can determine the number of children and adults at the public pool using a system of equation, where:
- C represents the number of children,
- and A represents the number of adults.
First equation:
Since there were 298 people at the pool, our first equation is given by:
C + A = 298
Second equation:
We know that the revenue earned from the children and adult admission fees equals the total revenue of $478.50:
(children admission price * quantity) + (adult admission price * quantity) = 478.50
Since the price for children was $1.50 and the price for adults was $2.00, our second equation is given by:
1.50C + 2.00A = 478.50
Method to solve: Elimination:
Multiplying the first equation by -1.50C will allow us to eliminate C since -1.50C + 1.50C = 0:
-1.50(C + A = 298)
-1.50C - 1.50A = -447
Solving for A:
Now we can add -1.50C - 1.50A = -447 to the second equation (i.e., 1.50C + 2.00A = 478.50) to eliminate C and solve for A:
-1.50C - 1.50A = -447
+
1.50C + 2.00A = 478.50
----------------------------------------------------------------------------------------------------------(-1.50C + 1.50C) + (-1.50A + 2.00A) = (-447 + 478.50)
(0.50A = 31.50) / 0.50
A = 63
Thus, there were 63 adults at the public swimming pool.
Solving for C:
Now we can solve for C by plugging in 63 for A in the first equation (i.e., C + A = 298):
(C + 63 = 298) - 63
C = 235
Thus, there were 235 children at the public swimming pool.