# A group of friends share a bill for \$13.69 equally between them. How many were in the group?

jseligmann | Certified Educator

37 friends each contribute 37 cents.

A peculiar thing about the number 1369 is that it is the only four-digit square in which all the digits increase. This may not be a real big deal, but it's interesting. I wonder if it's just a coincidence that the 1369 Coffee Shop in Cambridge, Massachusetts is in Inman Square. Anyone, anyone?

krishna-agrawala | Student

The answer #1 posted above is correct but the reasoning for arriving at the answer is not given.

So solve the above question we first convert the total amount from dollars to cents. Thus

Amount spent in dollars = 13.69

Therefore: Amount spent in cents = 13.69*100 = 1369

Now

(Number of friends sharing the bill)*(Amount shared by each) = 1369

In the above equation both number of friends sharing the bill and amount shared by each must be whole numbers as people cannot be in fractions, and cent being the smallest coin available, amount in denominations smaller than a cent cannot be shared equally.

It so happens that there are only two factors of 1369. These are 37 and 37, or

1369 = 37*37

1369 is not divisible by any other whole number.

Therefore the number of friends has to be 37, and share of bill of each has to be 37 cents.

neela | Student

The number 1369 could be factored like: 1*1369 or 37*37.

Therefore the possible nummers are 1, 1369 and 37 each of which divides 1369 cents equally without remainder. Or

1369=1*1369 or 139=37*37. So,

1369/1 = 1369 and  1369/1369=1  or

1369/37 = 37.

So, having only one man group is a possible answer, but one man group looks little strange.

Having 1369 members is also possible and the bill could be shared equally each getting one cent. But the group is very large.

So the ideal number of men in the group is 37 , which may also be large,without any other better alternative, and each man gets 1369/37=37 cents as his equal share of the bill.