Final answer:
To determine the number of children's tickets sold, we can set up a system of linear equations with the total number of attendees (25,000) and the total earnings ($600,000) and then solve the matrix equation. This involves finding the inverse of the matrix for the constants (1,1 and 15,35) and applying it to the matrix for the totals (25,000 and 600,000).
Step-by-step explanation:
To solve for the number of children's tickets sold at the amusement park when the total attendance is 25,000 and the total money earned is $600,000, we can use a system of linear equations. We have two unknowns: the number of children, let's call that x, and the number of adults, which we'll call y. We can set up the following equations:
1) x + y = 25,000 (Total attendance)
2) 15x + 35y = 600,000 (Total money earned)
To solve the matrix equation:
A = \[\begin{pmatrix}1 & 1 \\ 15 & 35\end{pmatrix}\], B = \[\begin{pmatrix}25000 \\ 600000\end{pmatrix}\]
The solution is found by using the inverse of matrix A (if it exists) to multiply matrix B. This can be done using various mathematical tools or software.