# 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

$n e = 72 \ \\ (n-3)(e+4) = 72 \ \\ n = 9 \ \\ e = 8$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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