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? 1 Answer Mar 15, 2018 85 children and 135 adults Explanation: $\textcolor{b l u e}{\text{Setting up the initial conditions}}$Let the count of children be $c$Let the count of adults be $a$Then $c + a = 220 \leftarrow \text{ Ticket count}$$\implies c = 220 - a \text{ } \ldots \ldots \ldots \ldots \ldots \ldots E q u a t i o n \left(1\right)$($8xxc)+($10xxa)=$2030 larr" Cost count"

Dropping the $sign we have: $8 c + 10 a = 2030 \text{ } \ldots \ldots \ldots \ldots \ldots E q u a t i o n \left(2\right)$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{Answering the problem}}$Using $E q n \left(1\right)$substitute for $c$in $E q n \left(2\right)$color(green)(8color(red)(c)+10a=2030color(white)("ddd")->color(white)("ddd") 8(color(red)(220-a))+10a=2030 $\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("dd.d}} 1760 - 8 a + 10 a = 2030}$$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("dd.d}} 2 a = 2030 - 1760}$$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("dd.d}} a = \frac{270}{2} = 135}$Substitute for $a$in $E q n \left(2\right)$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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{Check}}$$85 + 135 = 220$as required 85($8)+135($10) =$2030 as required