240 people attended a concert.tickets for adults were R60 and for children R40. The concert raied R12800. How many adults and how many children attended???
Let's assume the number of adult attendees as 'A' and the number of children attendees as 'C'.
According to the given information, we can form two equations:
1) A + C = 240 (equation 1)
(The total number of attendees is 240.)
2) 60A + 40C = 12800 (equation 2)
(The total revenue from adult tickets is 60A, and the total revenue from children tickets is 40C.)
To solve these equations, we can use a method called substitution.
First, solve equation 1 for A:
A = 240 - C (equation 3)
Now, substitute equation 3 into equation 2:
60(240 - C) + 40C = 12800
Expanding the equation:
14400 - 60C + 40C = 12800
Combine like terms:
-20C = 12800 - 14400
-20C = -1600
Divide both sides by -20:
C = -1600 / -20
C = 80
Substitute C = 80 back into equation 3 to solve for A:
A = 240 - C
A = 240 - 80
A = 160
Therefore, there were 160 adults and 80 children who attended the concert.
To find the number of adults and children who attended the concert, we can use a system of equations.
Let's assume the number of adults who attended the concert is A, and the number of children is C.
From the given information, we know that the total number of people who attended the concert is 240:
A + C = 240 --- Equation 1
We also know that the total amount of money raised from ticket sales is R12800. The price of an adult ticket is R60, and the price of a children's ticket is R40. Therefore, the total amount raised can be calculated as follows:
60A + 40C = 12800 --- Equation 2
Now, we have a system of equations consisting of two equations:
A + C = 240 --- Equation 1
60A + 40C = 12800 --- Equation 2
We can solve this system of equations using various methods, such as substitution or elimination.
Let's solve using the elimination method.
Multiply Equation 1 by 40:
40A + 40C = 9600 --- Equation 3
Subtract Equation 3 from Equation 2:
60A + 40C - (40A + 40C) = 12800 - 9600
20A = 3200
Divide both sides by 20:
A = 3200 / 20
A = 160
Now substitute the value of A into Equation 1 to find the number of children:
160 + C = 240
C = 240 - 160
C = 80
Therefore, there were 160 adults and 80 children who attended the concert.
200 and 140
A = 240 - C
60A + 40C = 12,800
Substitute 240-C for A in the second equation and solve for C. Insert that value into the first equation to solve for A. Check by putting both values into the second equation.