Have you tried solving this system?
1340A+627K=13.5
1278K+593K=14.8
it does look like it would give a negative answer, are you sure the numbers in the question are correct?
I'm not 100% certain if this is the correct forum so please forgive me if it is better suited in another location but I am not certain exactly what kind of math would be involved in solving this issue and this forum seemed like the best fit.
Problem: Figure out how much of a specific product each guest will use, broken down by adults and kids.
Data: We have the total usage of a product, the number of adults, the number of kids, broken down by week.
Example:
Week 1: 1340 Adults and 627 Kids consumed 13.5 units of product x.
Week 2: 1278 Adults and 593 Kids consumed 14.8 units of product x.
From this data we can easily conclude how much of product x the average guest uses if we don't break down the guest count by adults and kids. However, I'm stuck trying to calculate the usage broken down by Kids and Adults. I've tried solving this using a system of equations and while I arrived at a mathematically correct solution it was obviously wrong from a logical standpoint (one of the variables ended up negative which would indicate that a guest was giving the business a certain amount of product x).
With the data I have is it even possible to calculate this? If so what method would be best suited to solving this type of problem. If this isn't possible what additional data would I need to be able to calculate this?
Thanks.
Have you tried solving this system?
1340A+627K=13.5
1278K+593K=14.8
it does look like it would give a negative answer, are you sure the numbers in the question are correct?
Yeah when solving that system I ended up with the values: 0.190562 and -0.385731. The numbers given are accurate to the best of my knowledge. Are you aware of any other methods I can try besides a system of equations? Sadly math is not my strong suit and trying the system of equations was about the extent of my math knowledge in this area.
You have the right solution to the equations. There isn't much point in us reworking the answer in a different way because you obviously know how to solve simultaneous equations already. as pickslides suggests, your solution is unique and no method exists which will give a different one.
However, if you have a silly answer, it may be that your equations implicitly include an incorrect assumption.
I think you have assumed that the average for kids and adults is the same in week 1 and week 2. this is clearly not the case as in week 2 you have fewer kids, and fewer adults, but more sales.