SOLUTION: mr thomas and his three children paid a total of $65.75 for admission to water world. mr and mrs li and her six children paid a total of $131.50. what is the price of an adults tic

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Question 1208700: mr thomas and his three children paid a total of $65.75 for admission to water world. mr and mrs li and her six children paid a total of $131.50. what is the price of an adults ticket and what is the price of a children's ticket
Found 3 solutions by ikleyn, Edwin McCravy, timofer:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
mr thomas and his three children paid a total of $65.75 for admission to water world.
mr and mrs li and her six children paid a total of $131.50.
what is the price of an adults ticket and what is the price of a children's ticket
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As worded, printed, posted and presented, this problem can not be solved
and the question can not be answered.

It is so, because the second scenario is precisely doubled first scenario,
both from the point of participants and from the point of the total cost.

So, we have two unknowns, but only one independent equation for them,
which is not enough to answer the question.



Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
system%28A%2B3C=65.75%2C2A%2B6C=131.50%29

The second equation is equivalent to the first (multiplied by 2)
Therefore the system is dependent. If the prices are an integer
number of pennies, then consider $65.75 as 6575 pennies.

A=6575-3C

6575-3C must be an integer, say I

A=6575-3C=I

Divide through by 3

6575%2F3-3C%2F3=I%2F3

2191%262%2F3-C=I%2F3

2191%2B2%2F3-C=I%2F3

Isolate fraction terms

2191-C=I%2F3-2%2F3

The left side is an integer so the right side must be also, say integer N

I%2F3-2%2F3=N  and 2191-C=N, so C=N%2B2191

I-2=3N

I=3N%2B2

A=6575-3C=I=3N%2B1

Solutions:  A=3N%2B1 and C=N%2B2191 , Where A and C are in cents.

If adults' tickets are to be realistically more expensive than children's tickets, then A > C

3N%2B1%3EN%2B2191
2N%3E2190
N%3E1095

So N would have to be greater than 1095 for adults' tickets to be realistically
more expensive than childrens' tickets.

Edwin

Answer by timofer(104) About Me  (Show Source):
You can put this solution on YOUR website!
The Thomas group, a adult price and c children price
a%2B3c=65.75

The Li family
2a%2B6c=131.50

Not enough information in the description to find the ticket prices for adult and child.
Both equations are equivalent to a%2B3c=65.75.
You can look for some possibilities.