SOLUTION: If I could get help on this problem, I would be very grateful. The price to a child's admission to a broadway show is 50$. The price for adults is greater than 50$ but less than

Question 958448: If I could get help on this problem, I would be very grateful.
The price to a child's admission to a broadway show is 50$. The price for adults is greater than 50$ 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?
I was thinking of setting up two linear equations and using substitution since it looks like that sort of problem, but the wording is very confusing.
thank you very much :)
Found 2 solutions by rothauserc, Theo:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be the number of children and y be the number of adults, then
50x + (50 < c < 500)y = 28149
we are given x = 70
3500 + ( 50 < c < 500 )y = 28149
( 50 < c < 500 )y = 24649
note that the square root of 24649 is 157, therefore
157y = 24649
y = 157
157 adults attended and the cost of an adult ticket is $157

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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.

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