Respuesta :
Answer: 15 goodie bags. 4 chocolate bars, 2 peanut butter cups, and 3 hard candies per bag.
Step-by-step explanation: The factors of 60:
1 and 60
2 and 30
3 and 20
4 and 15
5 and 12
6 and 10
The factors of 30:
1 and 30
2 and 15
3 and 10
5 and 6
The factors of 45:
1 and 45
3 and 15
5 and 9
The greatest factors on the right (goodie bags) that are all the same is 15.
Answer:
- 15 bags
- 4 chocolate bars, 2 peanut butter cups, 3 bags hard candies
Step-by-step explanation:
You want to know the number of identical goodie bags that can be made from ...
- 60 chocolate bars
- 30 peanut butter cups
- 45 bags of hard candies.
Greatest common factor
The number of goodie bags that can be made is the greatest common factor of the numbers of each kind of goodie.
The greatest common factor of 30, 45, and 60 can be found several ways. One of them is to simply note that all of these numbers are multiples of 15.
Contents
The contents can be distributed among 15 goodie bags like this:
60c +30p +45b = 15(4c +2p +3b)
Each of the 15 goodie bags will contain ...
- 4 candy bars
- 2 peanut butter cups
- 3 bags of hard candies.
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Additional comment
One can find the GCF by looking at the factors of the numbers:
30 = 2·3·5
45 = 3·3·5
60 = 2·2·3·5
The factors common to all are 3·5 = 15.
One can also find the GCF using Euclid's algorithm. For 30 and 45, we have ...
45/30 = 1 r 15 . . . . . . the remainder replaces the larger number for the next step
30/15 = 2 r 0 . . . . . . . the 0 remainder tells you 15 is the GCF
Any factor of 30 is also a factor of 2·30 = 60, so we only need to look at 45 and 30.
We find it most convenient to make use of knowledge of multiplication tables. No calculation is involved if one can simply consult one's memory.
