Question 958448
The price of a child's admission to a broadway show is $50. 


The price for adult's admission is greater than $50 but less than $500 and is a whole number of dollars. 


If 70 children attend the show and the admission receipts total $28,149.00, how many adults attended? 


let x equal the price of an adult's ticket.


you have:


70 children attended.
the price of a child's ticket is $50.00
the price of all the tickets sold is equal to $28,149.00
you don't know how many adult tickets were sold.
let's call that y.


so x is the price of an adult's ticket and y is the number of adults.


the general equation would be:


price of a child's ticket * number of children that attended plus price of an adult's ticket * number of adults that attended equals the total price of all tickets sold.


you can replace what you know in this equation to get:


50 * 70 + x * y = 28,149.00


simplify this equation to get:


3500 + x * y = 28,149.00


subtract 3500 from both sides of this equation to get:


x * y = 28,149.00 - 3,500.00


simplify to get:


x * y = 24.649.00


we know that the price for adults is greater than 50 dollars but less than 500 dollars.


let's solve for y to get:


y = 24,649.00 / x


we know that x has to be between 50 and 500 dollars and we know that both y and x have to be integers.


x has to be integer because the number of adults has to be an integer.
y has to be an integer because the number of dollars has to be an integer as we are told.


i looked for numbers that divide into 24649 evenly and couldn't come up with any.


i then resorted to cheating by looking online to see if 24649 was prime or not.


it wasn't and online told me that it was divisible by 157.


that's your answer.


i graphed the equation so you could see.


<img src = "http://theo.x10hosting.com/2015/032502.jpg" alt="$$$" </>


i would like to think there was an easier way to find it but wasn't able to.


still, you have an answer, even though i had to go through hoops to get it.