#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#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Check")#

#85+135 = 220# as required

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