The distribution of candies

The distribution of candies

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I have a bag of candies to distribute among all my birthday attendees. If each one takes 6 candies, we have 5 left over and instead if we take 7 each one, we are missing 8.

How many are we on my birthday?


There are 83 candies and we are 13 assistants.
13 x 6 + 5 = 83. If we take 6 candies each of the 13 assistants left over 5.
13 x 7 - 8 = 83. If we take 7 candies each of the 13 assistants is missing 8.

To arrive at the solution, from the statement we obtain the following system of equations:
C = number of candies
X = numbers of attendees
C - 6X = 5
C - 7X = -8

If we solve the system we have that X = 13 and C = 83.