Question

a relief worker needs to divide 750 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?
□ boxes with □ bottles of water each and □ boxes with □ cans of food each

Explanation:

Step1: Find GCD of 750 and 324

To find the greatest common divisor (GCD) of 750 and 324, we use the Euclidean algorithm.
First, divide 750 by 324: \(750 = 324\times2 + 102\)

Step2: Divide 324 by 102

Next, divide 324 by 102: \(324 = 102\times3 + 18\)

Step3: Divide 102 by 18

Then, divide 102 by 18: \(102 = 18\times5 + 12\)

Step4: Divide 18 by 12

Next, divide 18 by 12: \(18 = 12\times1 + 6\)

Step5: Divide 12 by 6

Finally, divide 12 by 6: \(12 = 6\times2 + 0\)
When the remainder is 0, the divisor (6) is the GCD.

Step6: Find number of boxes for water

Number of boxes for water: \(750\div6 = 125\)

Step7: Find number of boxes for food

Number of boxes for food: \(324\div6 = 54\)

Answer:

125 boxes with 6 bottles of water each and 54 boxes with 6 cans of food each