Question

A club sells tickets to a event for $8 for children and $10 for adults. If they sold 220 tickets and the total amount received from tickets sales was $2030, how many children tickets and how many adult tickets were sold?

Answer 1

85 children and 135 adults

Explanation:

`color(blue)("Setting up the initial conditions")`

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

Then `c+a=220 larr" Ticket count"`

`=>c=220-a" "..................Equation(1)`

`($8xxc)+($10xxa)=$2030 larr" Cost count"`

Dropping the $ sign we have:

`8c+10a=2030" "...............Equation(2)`
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`color(blue)("Answering the problem")`

Using `Eqn(1)` substitute for `c` in `Eqn(2)`

`color(green)(8color(red)(c)+10a=2030color(white)("ddd")->color(white)("ddd") 8(color(red)(220-a))+10a=2030`

`color(green)(color(white)("dddddddddddddddd")->color(white)("dd.d")1760-8a+10a=2030)`

`color(green)(color(white)("dddddddddddddddd")->color(white)("dd.d")2a=2030-1760)`

`color(green)(color(white)("dddddddddddddddd")->color(white)("dd.d")a=270/2=135)`

Substitute for `a` in `Eqn(2)` giving:

`color(green)(8c+10 color(red)(a)=2030 color(white)("ddd")->color(white)("ddd")8c+10(color(red)(135))=2030`

`color(green)(color(white)("dddddddddddddddd")->color(white)("dd.d") c=(2030-1350)/8 =85`
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`color(blue)("Check")`

`85+135 = 220` as required

`85($8)+135($10) = $2030` as required