A miniature golf course charges different prices for adults and children. On Saturday, 50 adults and 50 children played, and the golf course earned $800. On Sunday, 65 adults and 75 children played, and the golf course earned $1,100. How much does the golf course charge for adults?
Let A be the cost for adults and C be the cost for children.
On Saturday the equation is 50A + 50C = $800.
On Sunday the equation is 65A + 75C = $1100.
Multiply the first equation by 65/50: (65/50)*(50A) + (65/50)*(50C) = (65/50)*$800
65A + (65/50)*50C = (65/50)*$800
65A + 65C = (65/50)*$800
65A + 65C = $1040
Multiply the second equation by -50/75: -(50/75)*(65A) - (50/75)*(75C) = -(50/75)*$1100
- (65/3)A - (50/75)*75C = -(50/75)*$1100
- (65/3)A - 65C = -(2/3)*$1100
- (65/3)A - 65C = -$733.33...
Combine like terms in both equations:
65A + 65C = $1040
- (65/3)A - 65C = -$733.33...
Add the two equations together: (65A + 65C) + (-(65/3)A - 65C) = $1040 + (-$733.33...)
(65A - (65/3)A) + (65C - 65C) = $1040 - $733.33...
((65 * 3)A - 65A) = $1040 - $733.33...
195A - 65A = $1040 - $733.33...
130A = $306.66...
Divide both sides by 130: A = $2.35. Answer: \boxed{2.35}.