Thread: primes and divisibility

I am having trouble in my new math course understanding what is going on. i do not know where to start on this problem i attached

Hello, ihavvaquestion!

This more of a math puzzle then a "real" math problem.

Someone spilled ink on a bill for 36 sweatshirts.
The result looked like the following.
There is one digit missing in front of the 8 and one digit missing after the 9.
The cost per shirt was not a frational part of a penny.

How much did each sweatshirt cost?
Find all possible costs per sweatshirt.


. .

Since the Total is a multiple of 4, it must end in a two-digit number divisible by 4.
. . There are two choices: .


Since the Total is a multiple of 9, the sum of its digits must be a multiple of 9.


If the Total is , the Total must be

. . Then: .


If the Total is , the Total must be

. . Then: .


Therefore, the unit price is either: .

2 questions...

how do you know the total is a multiple of four? is it because 36 is divisible by 4?

also, what total is divisible by 9? the 36 shirts?