Question 773387
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Tickets at fantasy land amusement park are 20 dollars for children and 30 dollars for adults. 6th grade students at Midtown middle school have an end-of-year class party at fantasy land. The students buy children tickets and the teachers/chaperones buy adult tickets. Altogether they buy a total of 110 tickets and the total cost is 2,290 dollars. How many of each ticket did they buy?
Ans:
Let the number of children be x
Then the number of adults = 110 - x (since they bought a total of 110 tickets)
Cost of children's tickets = 20*x
Cost of adult's tickets = (110 - x)*30
Total cost = {{{20*x + (110 - x)*30 = 2290}}}
{{{20*x + 3300 - 30*x = 2290}}}
Simplifying
{{{10*x = 3300 - 2290 = 1010}}} or {{{x = 101}}}
Number of children = {{{highlight(101)}}}
Number of adults = 110 - 101 = {{{highlight(9)}}}
Check for correctness:
Cost of children tickets = 101*20 = 2020
Cost of adult tickets = 9*30 = 270
Total = 2020 + 270 = 2290 (correct!)
:)
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