Final answer:
The solution to the system of equations representing the school athletic director's purchases is (14.515, 111.68).
Step-by-step explanation:
To find the solution to the system of equations, we can use the method of substitution or elimination. Let's first use the method of substitution:
From the first equation, we can express one variable in terms of the other. Let's solve for x:
10x + 5y = 703.55 --> 10x = 703.55 - 5y --> x = (703.55 - 5y)/10
Now we substitute this expression for x into the second equation:
18.50((703.55 - 5y)/10) + 11.99y = 703.55
Solving for y:
12910.45 - 92.50y + 11.99y = 7035.50 - 59.95y + 11.99y --> 52.51y = 5874.95 --> y = 111.68
Now substitute this value of y back into the first equation to find x:
10x + 5(111.68) = 703.55 --> 10x + 558.40 = 703.55 --> 10x = 145.15 --> x = 14.515
Therefore, the solution to the system of equations is (14.515, 111.68).