Multiple Choice Question
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 say the cost of an adult ticket is x dollars and the cost of a child ticket is y dollars.
From the first statement "On Saturday, 50 adults and 50 children played, and the golf course earned $800", we can create the equation:
50x + 50y = 800.
From the second statement "On Sunday, 65 adults and 75 children played, and the golf course earned $1,100", we can create another equation:
65x + 75y = 1100.
To solve these equations, we can use the method of elimination.
Multiplying the first equation by 13 and the second equation by 10 will allow us to eliminate the x terms:
(13)(50x + 50y) = (13)(800) => 650x + 650y = 10,400,
(10)(65x + 75y) = (10)(1100) => 650x + 750y = 11,000.
Now we subtract the two equations to eliminate the x terms:
650x + 750y - (650x + 650y) = 11,000 - 10,400,
100y = 600,
y = 6.
Substituting this value back into the first equation, we can solve for x:
50x + 50(6) = 800,
50x + 300 = 800,
50x = 500,
x = 10.
Therefore, the golf course charges $10 for adults. The answer is C.