Sports games

Pupils of the same school participated in district sports games. When dividing into teams found that in the case of the creative teams with four pupils remaining one pupil, in the case of five-member teams with remaining two pupils, and in the case of six-members teams with remaining three pupils. How many pupils in this school attended games if one school could participate a maximum of 80 pupils?

Correct answer:

n =  57

Step-by-step explanation:

0 = 4×0 + 0 = 5×0 + 0 = 6×0 + 0
1 = 4×0 + 1 = 5×0 + 1 = 6×0 + 1
2 = 4×0 + 2 = 5×0 + 2 = 6×0 + 2
3 = 4×0 + 3 = 5×0 + 3 = 6×0 + 3
4 = 4×1 + 0 = 5×0 + 4 = 6×0 + 4
5 = 4×1 + 1 = 5×1 + 0 = 6×0 + 5
6 = 4×1 + 2 = 5×1 + 1 = 6×1 + 0
7 = 4×1 + 3 = 5×1 + 2 = 6×1 + 1
8 = 4×2 + 0 = 5×1 + 3 = 6×1 + 2
9 = 4×2 + 1 = 5×1 + 4 = 6×1 + 3
10 = 4×2 + 2 = 5×2 + 0 = 6×1 + 4
11 = 4×2 + 3 = 5×2 + 1 = 6×1 + 5
12 = 4×3 + 0 = 5×2 + 2 = 6×2 + 0
13 = 4×3 + 1 = 5×2 + 3 = 6×2 + 1
14 = 4×3 + 2 = 5×2 + 4 = 6×2 + 2
15 = 4×3 + 3 = 5×3 + 0 = 6×2 + 3
16 = 4×4 + 0 = 5×3 + 1 = 6×2 + 4
17 = 4×4 + 1 = 5×3 + 2 = 6×2 + 5
18 = 4×4 + 2 = 5×3 + 3 = 6×3 + 0
19 = 4×4 + 3 = 5×3 + 4 = 6×3 + 1
20 = 4×5 + 0 = 5×4 + 0 = 6×3 + 2
21 = 4×5 + 1 = 5×4 + 1 = 6×3 + 3
22 = 4×5 + 2 = 5×4 + 2 = 6×3 + 4
23 = 4×5 + 3 = 5×4 + 3 = 6×3 + 5
24 = 4×6 + 0 = 5×4 + 4 = 6×4 + 0
25 = 4×6 + 1 = 5×5 + 0 = 6×4 + 1
26 = 4×6 + 2 = 5×5 + 1 = 6×4 + 2
27 = 4×6 + 3 = 5×5 + 2 = 6×4 + 3
28 = 4×7 + 0 = 5×5 + 3 = 6×4 + 4
29 = 4×7 + 1 = 5×5 + 4 = 6×4 + 5
30 = 4×7 + 2 = 5×6 + 0 = 6×5 + 0
31 = 4×7 + 3 = 5×6 + 1 = 6×5 + 1
32 = 4×8 + 0 = 5×6 + 2 = 6×5 + 2
33 = 4×8 + 1 = 5×6 + 3 = 6×5 + 3
34 = 4×8 + 2 = 5×6 + 4 = 6×5 + 4
35 = 4×8 + 3 = 5×7 + 0 = 6×5 + 5
36 = 4×9 + 0 = 5×7 + 1 = 6×6 + 0
37 = 4×9 + 1 = 5×7 + 2 = 6×6 + 1
38 = 4×9 + 2 = 5×7 + 3 = 6×6 + 2
39 = 4×9 + 3 = 5×7 + 4 = 6×6 + 3
40 = 4×10 + 0 = 5×8 + 0 = 6×6 + 4
41 = 4×10 + 1 = 5×8 + 1 = 6×6 + 5
42 = 4×10 + 2 = 5×8 + 2 = 6×7 + 0
43 = 4×10 + 3 = 5×8 + 3 = 6×7 + 1
44 = 4×11 + 0 = 5×8 + 4 = 6×7 + 2
45 = 4×11 + 1 = 5×9 + 0 = 6×7 + 3
46 = 4×11 + 2 = 5×9 + 1 = 6×7 + 4
47 = 4×11 + 3 = 5×9 + 2 = 6×7 + 5
48 = 4×12 + 0 = 5×9 + 3 = 6×8 + 0
49 = 4×12 + 1 = 5×9 + 4 = 6×8 + 1
50 = 4×12 + 2 = 5×10 + 0 = 6×8 + 2
51 = 4×12 + 3 = 5×10 + 1 = 6×8 + 3
52 = 4×13 + 0 = 5×10 + 2 = 6×8 + 4
53 = 4×13 + 1 = 5×10 + 3 = 6×8 + 5
54 = 4×13 + 2 = 5×10 + 4 = 6×9 + 0
55 = 4×13 + 3 = 5×11 + 0 = 6×9 + 1
56 = 4×14 + 0 = 5×11 + 1 = 6×9 + 2
57 = 4×14 + 1 = 5×11 + 2 = 6×9 + 3

n=4x+1=5y+2=6z+3 x,y,zN n80 n=57



Did you find an error or inaccuracy? Feel free to write us. Thank you!



Showing 1 comment:
Hold Up Wait A Minute
i like this





Tips for related online calculators
Do you want to perform natural numbers division - find the quotient and remainder?

Related math problems and questions: