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?
Set up two equations
a = adults
c = children
70a + 40c = 27750
a + c = 450
Solve by substitution or elimination
Substitution:
70a + 40c = 27750
a = 450 - c
Elimination:
70a + 40c = 27750
-70(a + c) = -70(450)
To determine how much of each ticket was sold, we can use a system of equations. Let's define two variables:
Let x be the number of adult tickets sold.
Let y be the number of children's tickets sold.
From the information given, we can form two equations:
1) The total number of tickets sold is 450:
x + y = 450 (Equation 1)
2) The total sales amount is $27,750:
70x + 40y = 27750 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use substitution to solve the system:
1) Solve Equation 1 for x:
x = 450 - y
2) Substitute the value of x into Equation 2:
70(450 - y) + 40y = 27750
Simplify the equation:
31500 - 70y + 40y = 27750
-30y = 27750 - 31500
-30y = -3750
Divide both sides by -30 to solve for y:
y = (-3750) / (-30)
y = 125
Now that we know the value of y, we can substitute it back into Equation 1 to find x:
x + 125 = 450
x = 450 - 125
x = 325
Therefore, 325 adult tickets and 125 children's tickets were sold.