Question 109402: Tickets for an event cost $5 for children, $11 for adults, and $6 for senior citizens. The total ticket sales were $1750. There were 50 more adult tickets sold than child tickets, and the number of senior citizens tickets were 4 times the number of child tickets. How many of each ticket were sold?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=number of children tickets sold
And y=number of adult tickets sold
And z=number of senior tickets sold
Now the problem tells us the following:
5x+11y+6z=1750-------------------------------eq1
and
y=x+50------------------------------------------eq2
and
z=4x----------------------------------------------eq3
Three equations, three unknowns. Lets solve by substitution. We will substitute the value for y in eq2 and the value for z in eq3 into eq1 and we get:
5x+11(x+50)+6(4x)=1750 get rid of parens
5x+11x+550+24x=1750 subtract 550 from both sides
5x+11x+550-550+24x=1750-550 collect like terms
40x=1200 divide both sides by 40
x=30------------------------------------number of children tickets sold
substitute x=30 into eq2:
y=30+50=80-----------------------------number of adult tickets sold
substitute x=30 into eq3 and we have:
z=4*30=120------------------------------number of senior tickets sold
CK
From eq1:
5*30+11*80+6*120=1750
150+880+720=1750
1750=1750
Hope this helps---ptaylor
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