The grade four pupils donated 125 cup noodles and 140 packs of canned goods for the Alay Kapwa project of their school. They want to pack these in plastic bags with the same number of cup noodles and canned goods in each bag. What is the greatest number of canned goods and cup noodles that can be placed in the plastic bags? How many bags do they need?
GCD(125,140) = 5
so, 25 bags with 5 noodles and 5 cans
and 15 cans left over
i thought it was GCF
Well, it looks like the grade four pupils are quite generous with their donations! Let's see if we can figure out the best way to pack these items.
To find the greatest number of canned goods and cup noodles that can be placed in the bags, we need to find their greatest common divisor (GCD). The GCD of 125 and 140 is 5. So, each bag can have 5 cup noodles and 5 canned goods.
To calculate the number of bags needed, we can divide the total number of items by the number of items per bag. The pupils donated a total of 125 cup noodles and 140 canned goods, so we'll need 125/5 = 25 bags for the cup noodles and 140/5 = 28 bags for the canned goods.
That means the grade four pupils will need 25 bags for the cup noodles and 28 bags for the canned goods. And of course, we hope they don't forget to write a funny joke or two on each bag to bring some extra smiles to the recipients!
To find the greatest number of canned goods and cup noodles that can be placed in the plastic bags, we need to find the greatest common divisor (GCD) of 125 and 140.
To find the GCD, we can use the Euclidean algorithm:
Step 1: Divide 140 by 125.
140 ÷ 125 = 1 remainder 15
Step 2: Divide 125 by 15.
125 ÷ 15 = 8 remainder 5
Step 3: Divide 15 by 5.
15 ÷ 5 = 3
Step 4: Since the remainder is now 0, we stop.
The GCD of 125 and 140 is 5.
Therefore, the greatest number of canned goods and cup noodles that can be placed in each plastic bag is 5.
Now, to find the number of bags needed, we divide the total number of items (125 + 140 = 265) by the number of items in each bag (5).
265 ÷ 5 = 53
Therefore, the pupils will need 53 bags to pack all the donated items.
To find the greatest number of canned goods and cup noodles that can be placed in the plastic bags, we need to find the greatest common divisor (GCD) of 125 and 140.
1. Begin by listing the factors of each number:
Factors of 125: 1, 5, 25, 125
Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
2. Identify the common factors of both numbers:
Common factors of 125 and 140: 1, 5
3. Determine the GCD, which is the largest common factor:
GCD(125, 140) = 5
Therefore, the greatest number of canned goods and cup noodles that can be placed in the plastic bags is 5.
To find the number of bags needed, we divide the total quantity of donated items by the GCD:
Number of bags = Total quantity / GCD(125, 140)
= (125 + 140) / 5
= 265 / 5
= 53
Therefore, they need 53 plastic bags to pack the donated items. Each bag will contain 5 cup noodles and 5 canned goods.