The treasurer of the student body at a college reported that the receipts from a recent contact totaled $916; Furthermore, he announced that 560 people had attended the concert. Students were charged $1.25 each for admission to the concert, and adults were charged $2.25 each. How many adults attended the concert?
Let's assume the number of adults who attended the concert is A.
Given:
Total receipts = $916
Number of students = 560
Student admission price = $1.25
Adult admission price = $2.25
Now, we can set up an equation based on the given information:
1.25 * 560 + 2.25 * A = 916
Simplifying the equation:
700 + 2.25A = 916
Subtracting 700 from both sides:
2.25A = 216
Dividing both sides by 2.25:
A = 96
Therefore, there were 96 adults who attended the concert.
To solve this problem, we can use a system of equations. Let's assume that the number of adults who attended the concert is A and the number of students is S.
From the given information, we can write two equations:
1) The total receipts from the concert were $916:
$1.25S + $2.25A = $916
2) The total number of people who attended the concert was 560:
S + A = 560
To solve this system of equations, we can use substitution or elimination method. Let's use elimination:
Multiply equation 2 by 1.25 to make the coefficients of S in both equations the same:
1.25(S + A) = 1.25(560)
1.25S + 1.25A = 700
Now, subtract equation 1 from equation 3:
1.25S + 1.25A - 1.25S - 2.25A = 700 - 916
-1A = -216
Divide both sides of the equation by -1:
A = 216
Therefore, there were 216 adults who attended the concert.
a+c = 560
2.25a + 1.25c = 916
now just solve for a