A music concert was attended by 450 people. Adult tickets sold for $70 and children’s tickets for $40. If total sales were $27,750, how much of each ticket was sold?
Adult: a
Children: c
a + c = 450
70a + 40c = 27750
Substitute
c = 450 -a
70a + 40(450 - a) = 27750
70a + 18000 -40a = 27750
30a + 18000 = 27750
30a + 18000- 18000= 27750-18000
30a = 9750
30a/30 = 9750/30
a = 325
c = 450 -a
c = 450-325
c = 125
To determine how many adult and children's tickets were sold, we can set up a system of equations.
Let's assume that x represents the number of adult tickets sold and y represents the number of children's tickets sold.
Based on the given information, we can write the following equations:
Equation 1: x + y = 450 (since the total number of people who attended the concert is 450)
Equation 2: 70x + 40y = 27,750 (since the total sales from adult tickets at $70 each and children's tickets at $40 each is $27,750)
Now we can solve this system of equations to find the values of x and y.
We can use the substitution method to solve for x and y. Let's solve Equation 1 for x:
x = 450 - y
Substituting this value of x in Equation 2, we have:
70(450 - y) + 40y = 27,750
Now, we can distribute and simplify:
31,500 - 70y + 40y = 27,750
Combine like terms:
-30y = -3,750
Divide both sides by -30 to solve for y:
y = -3,750 / -30
y = 125
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
x + 125 = 450
x = 450 - 125
x = 325
Therefore, 325 adult tickets and 125 children's tickets were sold to reach a total sales of $27,750.