Question

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?

Answer 1

Answer:

the largest number of relief supply that can put in a box is  $T =7$

Step-by-step explanation:

From the question  we are told that

     The number of bottles to divide is $n = 810 \ bottles$

       The  number of  cans of food is $m = 324 \ cans$

 

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  

            $810 -324 * 1 =486$

            $486 - 324 * 1 = 162$

              $324 -162 * 1 = 162$

               $162 -162 * 1 = 0$

 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  $k = \frac{810}{162} = 5 \ bottles$

    The number of  cans of food in each box is $y = \frac{324}{162} = 2 \ cans$

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

            $T = k+ y$

            $T = 5 + 2$

            $T =7$