SOLUTION: A relief worker needs to divide 240 bottles of water and 144 cans of food into groups that each contain the same number of items. Also, each group must contain the same type of ite

Question 1013776: A relief worker needs to divide 240 bottles of water and 144 cans of food into groups that each contain the same number of items. Also, each group must contain the same type of item (bottled water or csnned food). What is the largest number of relief supplies that can be put into each group?

I need help please, much appreciated!!
Found 2 solutions by mathmate, josmiceli:
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
A relief worker needs to divide 240 bottles of water and 144 cans of food into groups that each contain the same number of items. Also, each group must contain the same type of item (bottled water or canned food). What is the largest number of relief supplies that can be put into each group?

Solution:
This problem is related to HCF (highest common factor).
The maximum number of groups is the HCF of 240 and 144.
The number of items in each group is 240 or 144 divided by the HCF.
To find the HCF of two numbers, we can either factor each number into powers of primes, and determine the maximum power of each prime factor that is common to both numbers, as follows:

Hence the HCF is
We calculate 240/48=5, 144/48=3,
So there can be a maximum of 48 groups, with 5 bottled water and 3 canned food.

Alternatively, we can find the HCF by the Euclid algorithm, which is taking the difference between the remainder of the large number divided by the small number, until the difference is 0.
240-144*1=96
144-96*1=48
96-48*1=48
48-48*1=0
so the HCF is 48.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If I read this right,

-----------------
It looks like you could have 3 groups with 48
cans of food and 3 groups with 48 bottles of water
That would give you the most items in each of
the 3 groups. Then there would be
bottles of water left over
--------------------------
So, the answer would be ( bottles and cans )
is the largest number of relief supplies that could be put
into each group.
------------------
Definitely get another opinion on this. It's kind of a strange question.
It sounds like they don't care how many groups there are.
Why would that be?
RELATED QUESTIONS
A relief worker needs to divide 900 bottles of water and 486 cans of food into groups... (answered by richwmiller)
A relief worker needs to divide 2250 bottles of water and 486 cans of food into groups... (answered by josmiceli)
you have organized a donation drive for the victims of typhoon odette. you are preparing... (answered by ikleyn)
Rico wants to divide 45 cans of sofa into two groups so that the ratio is 4 to 5. How... (answered by addingup)
Luke is helping to fill boxes for a canned-food drive. He has some total number of cans... (answered by josgarithmetic)
diane has a truck filled with cans that weigh 14 oz each and bottles that weigh 70 oz... (answered by richwmiller)
There are 60 boys and 72 girls in a school. The principal wants to divide the students... (answered by josgarithmetic)
A concession-stand manager buys bottles of water and soda to sell at a football game. The (answered by jorel1380)
Please help me? I don't understand this all that well. David has a job transporting... (answered by stanbon)