A relief worker needs to divide 810 bottles of water and 324 cans of food into boxes that each contain the same number of items. Also, each box must contain the same type of item (bottled water or canned food). What is the largest number of relief supplies that can be put in each box?

the largest number of relief supply that can put in a box is  

Step-by-step explanation:

From the question  we are told that

     The number of bottles to divide is

       The  number of  cans of food is

First we need to find the Highest common factor of 810  and  324

Applying the Euclid algorithm(This method involves subtracting the difference from the smallest number till the differerence is zero  )

   We have  

 Thus the HCF is  162

So the maximum number of boxes is  z =  162 boxes

   The number of bottles of water in each box is  

    The number of  cans of food in each box is

 Thus the largest number of relief supply that be put in the box is