**A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sandwiches cost $7.75 each and the soups cost $4.50 each. If the total cost of all 18 lunches was $113.50, how many sandwiches were ordered?
**

Ooh that's a tricky one. You can at least get a range for it...

You know that you have 18 people

You know that they each had one item, a soup or sandwich

You know the cost of sandwiches and soups

You know the total spent

So if everyone ordered sandwiches that would be (18 people)*($7.75), which is $139.50.

If everyone ordered soups, that would be (18 people)*($4.50), which is $81.00

You know it's somewhere in between there. The "Everyone had a sandwich" is closer to your goal, so you can start with that.

Then you look at the difference between the soup price and the sandwich price ($7.75-$4.50) = $3.25.

So you should be able to start with a sandwich for everyone = $139.50 and then subtract $3.25 a bunch of times until you get to your $113.50 answer. Each time you subtract $3.25 you're trading a sandwich for a soup because of the price difference between them.

If you want to do this with math, you could look at the difference between them...

$139.50 - $113.50 = $26.00

then divide that by $3.25 to get the number of soups...

Which I got a decimal number so I obviously messed up somewhere, but at least now you have a way to solve the problem :)

Edited August 10th, 2017
by Xhin