3/5 of the seats in a concert hall were occupied. The ratio of adults to children was 6:4. If 60 more adults attended the concert, the number of adults would be 3 times the number of children. How many seats were in the concert hall?
let x be the total no of seat
x=3/5
adult.....a
children....c
a/c=6/4.....(1)
a+60=3c.....(2)
a=6c/4.......(3)
insert 3 in any and find a....when u do finding won,t be a problem right
x=a+c....as total number
finding c i mean
Hmmm. The math looks right, but it turns out that the number of seats is not an integer.
??
To solve this problem, we need to break it down into separate steps.
Step 1: Determine the current number of adults and children at the concert.
Let's assume that there are 6x adults and 4x children at the concert. Since the ratio of adults to children is 6:4, we can represent the number of adults as 6x and the number of children as 4x.
Step 2: Calculate the total number of people at the concert.
The total number of people at the concert can be found by adding the number of adults and the number of children. So, the total number of people is 6x + 4x = 10x.
Step 3: Calculate the number of occupied seats.
If 3/5 of the seats were occupied, we can represent this as 3/5 * total number of seats = 10x.
Step 4: Find the total number of seats.
To find the total number of seats, we need to solve the equation:
(3/5) * total number of seats = 10x
To eliminate the fraction, we can multiply both sides of the equation by 5:
3 * total number of seats = 50x
Divide both sides by 3 to isolate the total number of seats:
total number of seats = (50x) / 3
Step 5: Find the number of seats when 60 more adults attend the concert.
If 60 more adults attend the concert, the new number of adults will be 6x + 60. The new number of children will remain the same as 4x. According to the problem, the number of adults will be 3 times the number of children. So, we can set up the equation:
6x + 60 = 3 * (4x)
Simplify the equation:
6x + 60 = 12x
Subtract 6x from both sides:
60 = 6x
Divide both sides by 6 to find the value of x:
x = 10
Step 6: Calculate the total number of seats using the value of x.
Substituting x = 10 into the equation for the total number of seats, we get:
total number of seats = (50 * 10) / 3
total number of seats = 500 / 3
total number of seats = 166.67 (approximated to the nearest whole number)
Therefore, there were approximately 167 seats in the concert hall.