Friends

Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?

Result

n =  9

Solution:

n=1 e=72(n-3).(e+4)=-152
n=2 e=36(n-3).(e+4)=-40
n=3 e=24(n-3).(e+4)=0
n=4 e=18(n-3).(e+4)=22
n=5 e=14.4(n-3).(e+4)=36.8
n=6 e=12(n-3).(e+4)=48
n=7 e=10.285714285714(n-3).(e+4)=57.142857142857
n=8 e=9(n-3).(e+4)=65
n=9 ****e=8(n-3).(e+4)=72
n=10 e=7.2(n-3).(e+4)=78.4
n=11 e=6.5454545454545(n-3).(e+4)=84.363636363636
n=12 e=6(n-3).(e+4)=90
n=13 e=5.5384615384615(n-3).(e+4)=95.384615384615
n=14 e=5.1428571428571(n-3).(e+4)=100.57142857143
n=15 e=4.8(n-3).(e+4)=105.6
n=16 e=4.5(n-3).(e+4)=110.5
n=17 e=4.2352941176471(n-3).(e+4)=115.29411764706
n=18 e=4(n-3).(e+4)=120
n=19 e=3.7894736842105(n-3).(e+4)=124.63157894737
n=20 e=3.6(n-3).(e+4)=129.2
n=21 e=3.4285714285714(n-3).(e+4)=133.71428571429
n=22 e=3.2727272727273(n-3).(e+4)=138.18181818182
n=23 e=3.1304347826087(n-3).(e+4)=142.60869565217
n=24 e=3(n-3).(e+4)=147
n=25 e=2.88(n-3).(e+4)=151.36
n=26 e=2.7692307692308(n-3).(e+4)=155.69230769231
n=27 e=2.6666666666667(n-3).(e+4)=160
n=28 e=2.5714285714286(n-3).(e+4)=164.28571428571
n=29 e=2.4827586206897(n-3).(e+4)=168.55172413793
n=30 e=2.4(n-3).(e+4)=172.8
n=31 e=2.3225806451613(n-3).(e+4)=177.03225806452
n=32 e=2.25(n-3).(e+4)=181.25
n=33 e=2.1818181818182(n-3).(e+4)=185.45454545455
n=34 e=2.1176470588235(n-3).(e+4)=189.64705882353
n=35 e=2.0571428571429(n-3).(e+4)=193.82857142857
n=36 e=2(n-3).(e+4)=198
n=37 e=1.9459459459459(n-3).(e+4)=202.16216216216
n=38 e=1.8947368421053(n-3).(e+4)=206.31578947368
n=39 e=1.8461538461538(n-3).(e+4)=210.46153846154
n=40 e=1.8(n-3).(e+4)=214.6
n=41 e=1.7560975609756(n-3).(e+4)=218.73170731707
n=42 e=1.7142857142857(n-3).(e+4)=222.85714285714
n=43 e=1.6744186046512(n-3).(e+4)=226.97674418605
n=44 e=1.6363636363636(n-3).(e+4)=231.09090909091
n=45 e=1.6(n-3).(e+4)=235.2
n=46 e=1.5652173913043(n-3).(e+4)=239.30434782609
n=47 e=1.531914893617(n-3).(e+4)=243.40425531915
n=48 e=1.5(n-3).(e+4)=247.5
n=49 e=1.469387755102(n-3).(e+4)=251.59183673469
n=50 e=1.44(n-3).(e+4)=255.68
n=51 e=1.4117647058824(n-3).(e+4)=259.76470588235
n=52 e=1.3846153846154(n-3).(e+4)=263.84615384615
n=53 e=1.3584905660377(n-3).(e+4)=267.92452830189
n=54 e=1.3333333333333(n-3).(e+4)=272
n=55 e=1.3090909090909(n-3).(e+4)=276.07272727273
n=56 e=1.2857142857143(n-3).(e+4)=280.14285714286
n=57 e=1.2631578947368(n-3).(e+4)=284.21052631579
n=58 e=1.2413793103448(n-3).(e+4)=288.27586206897
n=59 e=1.2203389830508(n-3).(e+4)=292.33898305085
n=60 e=1.2(n-3).(e+4)=296.4
n=61 e=1.1803278688525(n-3).(e+4)=300.45901639344
n=62 e=1.1612903225806(n-3).(e+4)=304.51612903226
n=63 e=1.1428571428571(n-3).(e+4)=308.57142857143
n=64 e=1.125(n-3).(e+4)=312.625
n=65 e=1.1076923076923(n-3).(e+4)=316.67692307692
n=66 e=1.0909090909091(n-3).(e+4)=320.72727272727
n=67 e=1.0746268656716(n-3).(e+4)=324.77611940299
n=68 e=1.0588235294118(n-3).(e+4)=328.82352941176
n=69 e=1.0434782608696(n-3).(e+4)=332.86956521739
n=70 e=1.0285714285714(n-3).(e+4)=336.91428571429
n=71 e=1.0140845070423(n-3).(e+4)=340.95774647887

ne=72 (n−3)(e+4)=72 n=9 e=8n e = 72 \ \\ (n-3)(e+4) = 72 \ \\ n = 9 \ \\ e = 8

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