The admission fee at an amusement park is $\$ 3.75$ for children and $\$ 5.60$ for adults. On a certain day, 219 people entered the park, and the admission fees collected totaled 1034 dollars. How many children and how many adults were admitted? number of children equals number of adults equals

Step 1 ：Let's denote the number of children as x and the number of adults as y. We know that the total number of people is 219, so we can write the first equation as \(x + y = 219\).

Step 2 ：We also know that the total admission fees collected is 1034 dollars, and since children's tickets cost $3.75 and adults' tickets cost $5.60, we can write the second equation as \(3.75x + 5.60y = 1034\).

Step 3 ：Now we have a system of two equations, which we can solve to find the values of x and y.

Step 4 ：Solving this system of equations, we find that \(x = 104\) and \(y = 115\).

Step 5 ：This means that 104 children and 115 adults were admitted to the amusement park.

Step 6 ：Final Answer: The number of children equals \(\boxed{104}\) and the number of adults equals \(\boxed{115}\).