grandma bought a big bag of candy. she divide the candy into ten equal packets for her ten grandchildren and one candy remained. when she heard that two grandchildren wouldn't come, she put all the candies back in the big bag and started over. she again made equal packets for the grand children who came and three candies remains. how much candy did grandma buy. if we know there were more than 200 and less than 260.
Answers
Given:
Grandma bought a big bag of candies. She divides the candies into ten equal groups for her ten grandchildren and one candy gets remained in this process. When two of her grandchildren weren't able to attend, Grandma decides to redistribute by taking back all the chocolates. Grandma equally divides the chocolates to the 8 grandchildren and 3 candies were left in this process. The number of candies near grandma is more than 200 and less than 260.
To Find:
The total number of candies grandma bought at the beginning.
Solution:
1. let the number of candies grandma initially purchased be x.
2. It is mentioned that the number of candies is greater than 200 and less than 260.
=> 200 > x > 260.
3. Initially, when the candies are distributed among 10 people, 1 candy is left after distribution. It simply implies the values of x which is greater than 200 and less than 260, which is divisible by 10 leaving the remainder as 1).
- Hence the possible values of x, in this case, are 201, 211, 221, 231, 241, 251.
4. In the second case, when the grandma redistributes the same number of chocolates among 8 people 3 chocolates will be remaining in this case. ( The values of x greater than 200 and less than 260, and are divisible by 8 leaving the remainder as 3).
- Hence the possible values of x, in this case, are 203, 211, 219, 227, 235, 243, 251, 259.
5. In both the cases the common values of x are 211 and 251. Hence the total number of chocolates in the bag which grandma bought, can have two values they are 211 and 251.
Therefore, the number of chocolates in the bag which grandma bought can be 211 and 251.
Number of candies can be 211 or 251
Given : Divided the candy into ten equal packets and one candy remained.
Divided the candy into 8 equal packets and three candy remained.
More than 200 candies but less than 260
To Find : Number of candies
Solution :
Assume that number of candies = N
N = 10A + 1 = 10A + 11 - 10 = 10(A - 1) + 11
N = 8B + 3 = 8B + 11 - 8 = 8 (B - 1) + 11
Hence N - 11 = 10(A - 1) = 8 (B - 1)
=> N - 11 is a multiple of 10 and 8 both
Multiple of 10 and 8 both will be multiple of LCM ( 10 , 8)
LCM - Least common multiplier of given numbers is the least number which is perfectly divisible by given numbers.
LCM = product of each factor of highest power
10 = 2 * 5
8 = 2 * 2 * 2
LCM ( 10 , 8) = 2 * 2 * 2 * 5 = 40
Multiples of 40
40 , 80 , 120 , 160 , 200 , 240 , 280
N - 11 = 200 or 240 will result in between 200 and 2600
=> N = 211 or 251
211 = 10 * 20 + 1
211 = 8 * 26 + 3
251 = 10 * 25 + 1
251 = 8 * 31 + 3
Number of candies can be 211 or 251
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