SOLUTION: Hello this is one of my practice problems before my test on wednesday...if you could please help me.... it would be great...thanks=] second question=] The national touring compan

Question 361817: Hello this is one of my practice problems before my test on wednesday...if you could please help me.... it would be great...thanks=] second question=]
The national touring company of Sesame Street Live visited Seattle, Washington, last year. The producers held a special promotional ticket sale for one hour. During this time, adult tickets sold for $5, junior tickets (kids aged 8 to 16) sold for $2, and children's tickets (kids aged 0 to 8) sold for the ridiculously low price of 10 cents. During this sale, 120 tickets sold for exactly $120. How many of each kind of ticket were sold during the sale?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

At first blush, it looks like this cannot be solved with the information given because you can only write two equations where there are three variables. But once you realize that not only do all of the values have to be positive integers, the number of child tickets must be a multiple of 10. That is because the total amount taken in is in even dollars.

Now if 120 child tickets were sold, then the total amount taken in would be $12. Not enough.

If 110 child tickets were sold then the most that could have been taken in was 11 plus 50 = $61. Again, not enough.

100 child, 10 + 100 = 110. Not enough again.

90 child, 9 + 150 = 159. Ah ha...this has possibilities.

Let

represent adult tickets at $5 each. Let

represent junior tickets at $2 each.

Then if 90 child tickets were sold:

Multiply the first equation by -2 and add the two equations:

and

That's one possibility.

Let child tickets equal 80, then

Multiply the first equation by -2 and add the two equations:

No good because

has to be an integer.

Let child tickets equal 70, then

Multiply the first equation by -2 and add the two equations:

No good because

has to be an integer.

Let child tickets equal 60, then

Multiply the first equation by -2 and add the two equations:

No good because

has to be a positive integer.

Any smaller number of child tickets will result in a negative number of adult tickets.

Hence the only answer is 17 adult tickets (17 times 5 is $85), 13 Junior tickets for $26, and 90 child tickets for $9. 85 + 26 + 9 = 120 and 17 + 13 + 90 = 120
Checks.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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