Question

During a promotional weekend is State Fair gives a free admission to every set 175th person who enters the fair on Saturday there were 6742 people at the fair on Sunday 5487 people attending the fair how many people receive a free admission over the 2day?

Answer 1

The State Fair gave out `69` free tickets

Explanation:

The State Fair officials count off `175` people and give a free ticket.

Then they count off `175` more people and give a free ticket ... and on and on.

So divide the total number of people by `175` to find out how many groups of `175` they counted off.

1) Find how many people in all attended over the weekend

`color(white)(.)` `6742` people on Saturday
`color(white)(.)` `5487` people on Sunday
―――
`12229` people total attended over the weekend

2) Find how many groups of `175` people attended

`12229 -: 175`

`color(white)(....)` `69.88` groups of `175`

Answer:
The State Fair gave out `69` free tickets

`color(white)(............)` . . . . . . . . . . . .

`"Extra credit"`

They gave out `almost` `70` free tickets, but they didn't quite have enough people attending.

If only `21` more people had attended, the total would have been
`12250` -- exactly enough for a `70`th group of `175` to go through the gates.