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?
A.
$6
B.
$8
C.
$10
D.
$16
Let's assume the price for an adult is A and the price for a child is C.
From the information given, we can set up two equations:
50A + 50C = 800 (Saturday's equation)
65A + 75C = 1100 (Sunday's equation)
To solve the system of equations, we can multiply the first equation by 65 and the second equation by 50 to eliminate C:
3250A + 3250C = 52000 (Saturday's equation x 65)
3250A + 3750C = 55000 (Sunday's equation x 50)
Subtracting the two equations to eliminate A gives us:
500C = 3000
C = 6
Substituting this value into the first equation to solve for A gives us:
50A + 50(6) = 800
50A + 300 = 800
50A = 500
A = 10
Therefore, the golf course charges $10 for adults.
Answer: C. $10