Excel Math problem

Hi

I have a math challenge that proved to be to much for me. Anyone up for the challenge?

I need to build an Excel model that handles to split a groups total price to price per group member, given some parameters.

Group price: this is given in the model but can be any price.
Number of Adults in the group: this can be 0-300
Number of Children in the group: this can be 0-300
The price for a single child must be 20% below the price for an adult.

Ok an Example

We have agreed on the price 16650 sek for a group with 10 adults and 20 children. I can trial and error my way to that the price for an adult should be roughly 638 sek and 513 sek for a child. But this only applies for this input. I want to build the model so I can enter any number of adults and children and any total price and get the price per adult and child automatically.

x = adult price
y = child price = x*(1-20%) = x*80%

10 adults + 20 children = 16650
=> 10x + 20y = 16650
=> 10x + 20x*80% = 16650
=> x*(10+20*80%) = 16650
=> x*26 = 16650
=> x = 16650/26 = 640.38
=> y = x*80% = 16650/26 * 80% = 512.31

Hi

Thanks for all answers.

I am sorry, I was not clear when I started the thread.

My problem is that I want to build an model in Excel were I can insert 1) any value for the Group 2) any value for number of adults and 3) any value for Children and the model gives me the price per Child and price per adult with 20% price differenc (or as close to 20% we can come).

Here is my solution:

Excel Math problem.png

Thanks Josephteh, looks good!