Question

At the movie theater, child admission is $5.10 and adult admission is $9.10. On Monday, 151 tickets were sold for a total sales of $1030.10. How many adult tickets were sold that day?

Answer 1

Answer: 65 adult tickets were sold that day

Explanation:

Let's call:

c: number of child tickets sold on Monday.

a: number of adult tickets sold on Monday.

Set up the following system of equations:

`\left \{ {{c+a=151} \atop {5.10c+9.10a=1030.10}} \right.`

You can solve it by Substitution method, as following:

- Multiply the first equation by -5.10

- Add both equations.

- Solve for a.

Then:

`\left \{ {{-5.10c-5.10a=-770.1} \atop {5.10c+9.10a=1030.10}} \right.\\---------\\4a=260\\a=65`

Answer 2

65

Explanation:

Let "a" represent the number of adult tickets sold. Then the number of child tickets sold is 151-a and the total revenue for the day is ...

9.10·a + 5.10·(151-a) = 1030.10

4a = 260 . . . . . . subtract 770.10

a = 65 . . . . . . . . . divide by 4

The number of adult tickets sold on Monday was 65.

_____

Check

65 adult tickets and 86 child tickets will produce a revenue of ...

65·9.10 + 86·5.10 = 591.50 + 438.60 = 1030.10 . . . . answer checks OK