Maybe something like:
200s + 105a + 200 = 1,000
You can use x and y instead of s for student and a for adult.
Are the adults and students charged the same? If so then:
200x + 105x + 200 = 1,000
I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:
![\displaystyle \frac{dV}{dr} = \lim_{h\to0} \frac{2\pi(r+h)^3-2\pi r^3}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdV%7D%7Bdr%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B2%5Cpi%28r%2Bh%29%5E3-2%5Cpi%20r%5E3%7D%7Bh%7D)
![\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{(r^3+3r^2h+3rh^2+h^3)- r^3}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdV%7D%7Bdr%7D%20%3D%202%5Cpi%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%28r%5E3%2B3r%5E2h%2B3rh%5E2%2Bh%5E3%29-%20r%5E3%7D%7Bh%7D)
![\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{3r^2h+3rh^2+h^3}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdV%7D%7Bdr%7D%20%3D%202%5Cpi%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B3r%5E2h%2B3rh%5E2%2Bh%5E3%7D%7Bh%7D)
![\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} (3r^2+3rh+h^2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdV%7D%7Bdr%7D%20%3D%202%5Cpi%20%5Clim_%7Bh%5Cto0%7D%20%283r%5E2%2B3rh%2Bh%5E2%29)
![\displaystyle \frac{dV}{dr} = 2\pi \cdot 3r^2 = \boxed{6\pi r^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdV%7D%7Bdr%7D%20%3D%202%5Cpi%20%5Ccdot%203r%5E2%20%3D%20%5Cboxed%7B6%5Cpi%20r%5E2%7D)
In Mathematica, you can check this result via
D[4/2*Pi*r^3, r]
They’ve already earned $105 so they need $45 more to reach their goal