The Badys and their maid, Alice, took a trip to Hawaii for their summer vacation. The travel agent told Ike that the trip would cost $210 for each child plus another $315 per adult. According to Ike Bady’s credit card receipt, the trip cost a total of $2205 for all 9 of them. Find the number of adults and children on the trip by writing a system of equations.

children --- x

adults -----9-x

210x + 315(9-x) = 2205
solve for x , should be straightforward.

BTW, $315 for a trip to Hawaii?
Time to update that Math textbook.

To solve this problem, we can create a system of equations based on the given information.

Let's assume the number of children on the trip is represented by 'c' and the number of adults is represented by 'a.'

From the given information, we know that the trip cost $210 per child and $315 per adult, and the total cost for all 9 people was $2205.

Equation 1: The cost for children: 210c
Equation 2: The cost for adults: 315a
Equation 3: The total cost for all people: 210c + 315a = 2205

Now, we need to find the values of 'c' and 'a' that satisfy this system of equations.

To do this, we can start by solving the third equation for 'c' in terms of 'a':

210c = 2205 - 315a
c = (2205 - 315a) / 210

Now, we can substitute this expression for 'c' into either Equation 1 or Equation 2 to solve for 'a' and then find 'c.'

Let's use Equation 1:

210c = 210c
210c = 210[((2205 - 315a) / 210)]
210c = 2205 - 315a
315a + 210c = 2205

Now we have a system of two equations:
Equation 3: 210c + 315a = 2205
Equation 4: 315a + 210c = 2205

We can solve this system of equations using the method of substitution or elimination. By solving this system, we will find the values of 'c' and 'a,' which represent the number of children and adults on the trip, respectively.