Esp At the movie theatre, child admission is $5.40 and adult admission is $9.80. On Wednesday, twice as many adult tickets as child tickets were sold, for a total sales of $875.00. How many child tickets were sold that day?

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xKelvin xKelvin · Answer 1 · 2020-09-21T23:37:45+02:00

Answer:

35 child tickets and 70 adult tickets.

Step-by-step explanation:

So, we know that a child ticket cost $5.40 and an adult ticket cost $9.80.

Let's let c denote the amount of child tickets and let's let a denote the amount of adult tickets.

On Wednesday, twice as many adult tickets as child tickets were sold. In other words:

[tex]a=2c[/tex]

Also, we know that the total sales that day was $875.00. So:

[tex]5.4c+9.8a=875[/tex]

5.4c represents the total sales from c child tickets, and the 9.8a represents the total sales from a adult tickets, for a total of 875 sales.

This is now a system of equations. We can solve it by substituting the first equation into the second.

Namely, substitute 2c for a. So:

[tex]5.4c+9.8(2c)=875[/tex]

Multiply:

[tex]5.4c+19.6c=875[/tex]

Combine like terms:

[tex]25c=875[/tex]

Divide both sides by 25:

[tex]c=35[/tex]

So, 35 child tickets were sold on Wednesday.

The amount of adult tickets sold was twice the amount of child tickets, so 35(2) or 70 adult tickets were sold.

And we're done!