a concert was held in a school. students tickets cost 5 dollars and regular cost 8 dollars. The school sold 284 tickets for 1600 dollars. Find the number of student tickets and the number of regular tickets sold.
5S+8R=1600
S+R=284
s=284-R
5(284-R)+8R=1600
5*284-5R+8R=1600
3R=1600-284*5
R=60
S=224
Let's assume the number of student tickets sold as 'S' and the number of regular tickets sold as 'R'.
Given:
1) Students tickets cost $5 each
2) Regular tickets cost $8 each
3) The school sold a total of 284 tickets
4) The total amount of money collected was $1600
From the given information, we can form the following equations:
1) S + R = 284 (Equation 1: Total number of tickets sold is 284)
2) 5S + 8R = 1600 (Equation 2: Total cost of tickets sold is $1600)
Now, we will solve these equations using the method of elimination or substitution.
Let's start with elimination:
Multiply Equation 1 by 5 and Equation 2 by -1 to eliminate 'S':
5S + 5R = 1420 (Multiply Equation 1 by 5)
-5S - 8R = -1600 (Multiply Equation 2 by -1)
Adding the above two equations, we get:
-3R = -180
Divide by -3 on both sides:
R = 60
Now, substitute the value of R in Equation 1:
S + 60 = 284
Subtract 60 from both sides:
S = 224
Therefore, the number of student tickets sold is 224, and the number of regular tickets sold is 60.
To solve this problem, we can use a system of equations. Let's assume that the number of student tickets sold is 's' and the number of regular tickets sold is 'r.'
We know that the total number of tickets sold is 284, so we can write the equation:
s + r = 284 --eq. (1)
We also know that the total revenue from ticket sales is $1600. Since each student ticket costs $5 and each regular ticket costs $8, we can write the second equation:
5s + 8r = 1600 --eq. (2)
To solve this system of equations, we can use the substitution or elimination method. Let's solve it using the elimination method.
To eliminate the 's' variable, let's multiply equation (1) by 5:
5s + 5r = 1420 --eq. (3)
Now, subtract equation (3) from equation (2) to eliminate the 's' variable:
(5s + 8r) - (5s + 5r) = 1600 - 1420
This simplifies to:
3r = 180
Divide both sides of this equation by 3:
r = 60
Substitute this value of 'r' into equation (1) to find the value of 's':
s + 60 = 284
s = 224
Therefore, the number of student tickets sold is 224 and the number of regular tickets sold is 60.