On a certain hot summer's day, 300 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The recipients for admissions totaled $613.50. How many children and how many adults swam at the public pool that day?
There were ___ children at the public pool.
There were ___ adults are the public pool.
2.25a + 1.75(300-a) = 613.5
To find the number of children and adults at the public pool, we can use a system of equations.
Let's assume the number of children at the pool is represented by C, and the number of adults is represented by A.
We know that the daily price for children is $1.75, so the total amount of money collected from children is 1.75C.
Similarly, the total amount of money collected from adults is 2.25A.
According to the given information, the total amount of money collected from admissions is $613.50.
So, we can write the equation: 1.75C + 2.25A = 613.50.
We are also given that the total number of people at the public pool is 300, so we can write another equation: C + A = 300.
Now, we have a system of equations:
1.75C + 2.25A = 613.50
C + A = 300
To solve this system of equations, we can use substitution, elimination, or any other method of solving simultaneous equations. Let's use the substitution method here.
From the second equation, we can express C in terms of A: C = 300 - A.
Substituting this expression for C in the first equation, we get:
1.75(300 - A) + 2.25A = 613.50
Now, we can solve for A:
525 - 1.75A + 2.25A = 613.50
0.50A = 613.50 - 525
0.50A = 88.50
A = 88.50 / 0.50
A = 177
Now, substitute the value of A back into the second equation to find the value of C:
C + 177 = 300
C = 300 - 177
C = 123
Therefore, there were 123 children and 177 adults at the public pool that day.
So, the answer is:
There were 123 children at the public pool.
There were 177 adults at the public pool.