Admission
to
a
movie
is
$11
for
adults
and
$8
for
children.
If
the
receipts
for
200
tickets
were
$1780,
how
many
adult
tickets
and
how
many
children’s
tickets
were
sold?
Let's assume that the number of adult tickets sold is represented by 'x' and the number of children's tickets sold is represented by 'y'.
According to the given information, the admission for adults is $11 and the admission for children is $8.
We can create two equations based on the given information:
1) x + y = 200 (Equation 1, representing the total number of tickets sold)
2) 11x + 8y = 1780 (Equation 2, representing the total revenue generated from ticket sales)
Now, we can solve this system of equations to find the values of 'x' and 'y'.
Using Equation 1, we can express 'x' in terms of 'y':
x = 200 - y
Substituting this value of 'x' into Equation 2:
11(200 - y) + 8y = 1780
2200 - 11y + 8y = 1780
-3y = -420
Dividing both sides by -3:
y = 140
Now, substitute this value of 'y' into Equation 1 to find 'x':
x + 140 = 200
x = 200 - 140
x = 60
Therefore, 60 adult tickets and 140 children's tickets were sold.
To determine the number of adult tickets and children's tickets sold, we will use algebraic equations.
Let's assume the number of adult tickets sold is "x" and the number of children's tickets sold is "y."
According to the given information:
- The price of an adult ticket is $11.
- The price of a children's ticket is $8.
- The total receipts for 200 tickets were $1780.
Now we can form two equations to solve for the values of "x" and "y."
Equation 1: x + y = 200 (since the total number of tickets sold is 200)
Equation 2: 11x + 8y = 1780 (since the total receipts were $1780)
We have a system of two equations with two variables. We can solve this system to find the values of "x" and "y."
One way to solve this system is by elimination or substitution. To use the substitution method, we will solve Equation 1 for either "x" or "y" and substitute that value into Equation 2.
Let's solve Equation 1 for "x":
x = 200 - y
Now substitute this value of "x" into Equation 2:
11(200 - y) + 8y = 1780
Distribute:
2200 - 11y + 8y = 1780
Combine like terms:
-3y + 2200 = 1780
Subtract 2200 from both sides:
-3y = 1780 - 2200
-3y = -420
Divide both sides by -3 to isolate "y":
y = -420 / -3
y = 140
Now, substitute the value of "y" back into Equation 1 to find "x":
x + 140 = 200
x = 200 - 140
x = 60
Therefore, 60 adult tickets and 140 children's tickets were sold.
If x adult tickets were sold, then 200-x child tickets were sold. So, add up the cost of each:
11x+8(200-x) = 1780
x = 60
so, 60 adult and 140 child tickets were sold.