Question 1158265: When the teacher divided her students into groups of four, she had three students remaining, when she divided them into groups of five , she had four students remaining. There were fewer than 40 students in the class. How many students could be in the class?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website! 19 students
Done using lists, very crude, not the best method
Better way is possible
DIV 4, r 3 DIV 5, r 4
7 9
11 14
15 19
19
23
First value found common to both is 19.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Let "n" be the unknown number under the question.
Add 1 (one) to the number, and consider N = n+1, instead of "n".
Then the number N is a multiple of 4 (OBVIOUS).
Also, the number N is a multiple of 5 (OBVIOUS).
The only numbers lesser than or equal to 40 and multiple to 4 and 5 are the numbers 20 and 40.
Returning from "N" to "n", we have, therefore, two answers for the given problem: 19 and 39.
Solved.
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For similar solved problems, see the lesson
- The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9
in this site.
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