Question 82389
x = no. of children; y = no. adults; z = no. of seniors
:
Write an equation for each sentence
Tickets for an event cost $5 for children, $10 for adults, and $8 for senior citizens. 
"The total ticket sales were $2060. "
5x + 10y + 8z = 2060
:
"There were 50 more adult tickets sold than child tickets,"
y = x + 50
:
"the number of senior citizens tickets were 3 times the number of child tickets"
z = 3*x
:
. How many of each ticket were sold? 
:
Notice that the last two equation put both y and z in terms x. Therefore if
we substitute for y and z in the total sales equation we can find x:
5x + 10(x+50) + 8(3x) = 2060
:
5x + 10x + 500 + 24x = 2060; multiplied what's in brackets
:
5x + 10x + 24x = 2060 - 500; subtracted 500 from both sides
:
39x = 1560
:
x = 1560/39
:
x = 40 children
:
Then:
y = x + 50
y = 40 + 50
y = 90 adults
:
And
z = 3*x
z = 2*40
z = 120 seniors
:
Check our solutions in the total sales equation:
5(40) + 90(10) + 8(120) =
200  +  900  + 960  = 2060