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
To solve this problem, we can set up a system of equations.
Let's represent the cost for adults as A and the cost for children as C.
From the given information, we can set up the following equations:
50A + 50C = 800 (equation 1)
65A + 75C = 1100 (equation 2)
To solve for A, we can solve the system of equations using substitution or elimination method.
Let's use elimination method:
Multiply equation 1 by 3 to get 150A + 150C = 2400 (equation 3)
Now, subtract equation 2 from equation 3:
150A + 150C - (65A + 75C) = 2400 - 1100
85A + 75C = 1300 (equation 4)
Now, subtract equation 1 from equation 4:
85A + 75C - (50A + 50C) = 1300 - 800
35A + 25C = 500 (equation 5)
Now we have a new equation with A and C only. Let's solve equation 5 for A:
35A + 25C = 500
35A = 500 - 25C
A = (500 - 25C) / 35
A = (100 - 5C) / 7
From the given answer choices, let's see which value for C will make A an integer:
A. $6
(100 - 5(6)) / 7 = 70 / 7 = 10 (which is an integer)
Therefore, the golf course charges $10 for adults. So, the correct answer is C. $10.