QuestionAt the movie theatre, child admission is $\$ 5.50$ and adult admission is $\$ 8.70$ . On Monday, 163 tickets were sold for a total sales of \$1139.70. How many adult tickets were sold that day?
Number of adult tickets: $\square$

Studdy Solution

STEP 1

1. Child admission costs \$5.50.
2. Adult admission costs \$8.70.
3. A total of 163 tickets were sold.
4. Total sales amounted to \$1139.70.
5. We need to find the number of adult tickets sold.

STEP 2

1. Define variables for the number of child and adult tickets.
2. Set up a system of equations based on the problem description.
3. Solve the system of equations to find the number of adult tickets.

STEP 3

Define variables.
Let $c$ be the number of child tickets sold, and $a$ be the number of adult tickets sold.

STEP 4

Set up a system of equations.
Equation 1: The total number of tickets sold is 163. $c + a = 163$
Equation 2: The total sales amount is \$1139.70. \[ 5.50c + 8.70a = 1139.70 \]

STEP 5

Solve the system of equations.
First, solve Equation 1 for $c$ : $c = 163 - a$
Substitute $c = 163 - a$ into Equation 2: $5.50(163 - a) + 8.70a = 1139.70$
Distribute the 5.50: $896.50 - 5.50a + 8.70a = 1139.70$
Combine like terms: $3.20a + 896.50 = 1139.70$
Subtract 896.50 from both sides: $3.20a = 243.20$
Divide both sides by 3.20 to solve for $a$ : $a = \frac{243.20}{3.20}$ $a = 76$
The number of adult tickets sold is:
$\boxed{76}$

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