Question

A relief worker needs to divide 900 bottles of water and 144 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? is the largest number of supplies that can be put in each box.

Answer 1

solution:

number of bottles need to devide = 900 bottles

number of cans devide = 144 cans

now we have to distribute equal amount of bottle in each group and equal amount of cans in each group

so to find the highest required number of groups to distribute equal amount of bottle and equal amount of can we have to take the highest common factor of 900 bottles and 144 cans

for 900 bottles, split it in possible factors

900 = 2*2*3*3*5*5

for 144 cans , split in possible factors

144 = 2*2*2*2*3*3

so common factors of split in both are 2*2*3*3 = 36

so the required number of groups = 36 so as to make the largest supply.

required number of groups = 36

each contain 900/36 = 25 bottles

144/36 = 4 cans