Question

Admission to a show costs $5 per child and $10 per adult. There were 15 more adults than twice the number of children at the last performance. If the total amount earned was $1700, how many children and adults attended?

Answer 1

`159" adults"`
`color(white)(1)22" children"`

Explanation:

Let the count of adults be `a`
Let the count of children be `c`

There were 15 more `............................?+15`
adults `.........................................a=?+15`
Than twice the number `..................a=(2xx?)+15`
of chidren `.....................................a=(2xx c)+15`

Write as `a=2c+15" "......Equation(1)`

Cost per child `=$5`
Cost per adult `=$10`

`color(blue)("Determine the count of children")`

Given that the total given revenue (earned) of `$1700` is from:

`color(white)("dd.ddddd")c color(white)("ddddddddddddddd")a=2c+15 larr Equation(1)`
`color(white)("ddddddd") darrcolor(white)("ddddddddddddddddddd")darr`
`(obrace("count of children")xx$5)+(obrace("count of adults")xx$10)`

`color(white)("dddddddd")$5c color(white)("dddddddd.d")+color(white)("dddd")$10(2c+15)color(white)("ddddd") =$1700`

`$5c+$20c+$150=$1700`

`$25c = $550`

Divide both sides by `$25`

`c=22 larr" Child count"`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the count of adults")`

Using relationship to cost

Total cost for children is `22xx$5=$110`

Cost for adults is `$1700-$110 = $1590`

Count of adults is how many lots of `$10` will fit into `$1590`

`cancel($1590)^159/(cancel($10)^1)`

`159" adults"`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Check")`

`(159xx$10)+(22xx$5)`

`$1590+$110=$1700`