Question

The admission prices for a small fair are $1.50 for children and $4.00 for adults. In one day there was $5050 collected. If we know that 2100 children paid admission, how many adults paid admission?

Answer 1

475 adults payed admissions on the give day.

Explanation:

We know that 2100 children paid admissions to the fair on the given day. If we take that amount and multiply it be the price per child for admissions, then we can figure out what part of the $5050 was admissions for children.

`2100*$1.50` = $3150

So $3150 of the $5050 was money gained because of children. To find the amount of money gained because of adults, we must subtract the money form children from the total amount of children and adults.

$5050-$3150 = $1900

$1900 was payed for because of adults. We also know that each adult admission ticket cost $4.00. Finally, we can divide the total amount of my gained from adults on the given day by the amount of one adults. this will give us the total number of adults at the fair on the given day.

`($1900)/($4.00)` = 475

So, there were 475 adults at the fair on that day.

Answer 2

Showing you some cheat type steps that will help you do things in your head without a calculator. You can scribble numbers down in the margin.

475 adults

Explanation:

`color(blue)("Determine the total cost of the children")`

`2100" children at "$1.50" each"`

2100 is the same as `21xx100`

So we have `21xx1.5xx100`

`color(brown)("Dealing with the 21 first")`

`21xx1.5 ->21`
`color(white)("dddddddd.d")ul(10.5 larr" Add")`
`color(white)("dddddddd.d")31.5`

`color(brown)("Now dealing with the "xx100)`

`31.50xx100= 3150 -> $3150.00`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the total cost of the addults")`

Total cost - cost of children = cost of adults

`$5050.00`
`ul($3150.00 larr" Subtract")`
`$1900.00 larr" From addults"`

`color(brown)("What follows is the doing in your head with scribbling bit")`

Each adult cost is $4.00 so it a matter of how many lots of $4.00 will fit into $1900.00

`1900 -: 4`

`1900xx1/4 larr" but "xx1/4" is the same as "xx1/2xx1/2`

`ubrace(1900xx1/2)xx1/2`
`color(white)("ddd")darr`
`color(white)("ddd")950color(white)("s.d")xx1/2`

But `950` is the same as `900+50`

So `950xx1/2` is the same as `ubrace((900xx1/2)+(50xx1/2))`

`color(white)("dddddddddddddddddddddddddd.ddd")450`
`color(white)("dddddddddddddddddddddddd.ddddd")ul(color(white)("d")25larr" Add")`
`color(white)("dddddddddd") " The count of adults" ->475`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Check")`

`color(white)("d")475xx$4.00= $1900.00`
`2100xx$1.50 =ul($3150.00larr" Add")`
`color(white)("ddddddddd.ddd")$5050.00`