At at basketball game,adult tickets were sold at $1.00 each and student tickets at 75c each. If 150 tickets were sold and $140 was collected,how many tickets of each kind were sold?
100 a + 75 s = 14000 pennies
a+s = 150 so a = 150-s
100(150 - s) + 75 s = 14000
15000 - 25 s = 14000
1000 = 25 s
s = 40
then a = 150 - 40 = 110
To solve this problem, we can use a system of linear equations. Let's assume the number of adult tickets sold is represented by 'a', and the number of student tickets sold is represented by 's'.
We are given two pieces of information:
1. Adult tickets were sold for $1.00 each.
2. Student tickets were sold for 75c each.
From the first piece of information, we can determine that the total revenue from adult tickets is 1.00 * a.
From the second piece of information, we can determine that the total revenue from student tickets is 0.75 * s.
The total number of tickets sold is 150, so we can write the equation:
a + s = 150 ----(Equation 1)
The total revenue collected is $140, so we can write another equation:
1.00 * a + 0.75 * s = 140 ----(Equation 2)
Now, we have a system of two equations:
Equation 1: a + s = 150
Equation 2: 1.00 * a + 0.75 * s = 140
We can solve this system of equations using any method, such as substitution or elimination. Let's use the substitution method.
First, we solve Equation 1 for 'a' in terms of 's':
a = 150 - s
We substitute this value of 'a' into Equation 2:
1.00 * (150 - s) + 0.75 * s = 140
Now, we simplify and solve for 's':
150 - s + 0.75s = 140
0.25s = 10
s = 40
Now that we know 's' is 40, we can substitute this value back into Equation 1 to find 'a':
a + 40 = 150
a = 150 - 40
a = 110
Therefore, 110 adult tickets and 40 student tickets were sold at the basketball game.