Megapizza

Megapizza will be divided among 100 people. First gets 1%, 2nd 2% of the remainder, 3rd 3% of the remainder, etc. Last 100th 100% of the remainder. Which person got the biggest portion?

Correct answer:

n =  10

Step-by-step explanation:

r1=1100 1=0.01 r2=2100 0.99=995000=0.0198 r3=3100 0.97020.0291 r4=4100 0.9410940.0376 r5=5100 0.903450240.0452 r6=6100 0.8582777280.0515 r7=7100 0.806781064320.0565 r8=8100 0.75030638981760.06 r9=9100 0.690281878632190.0621 r10=10100 0.628156509555290.0628 r11=11100 0.565340858599770.0622 r12=12100 0.503153364153790.0604 r13=13100 0.442774960455340.0576 r14=14100 0.385214215596140.0539 r15=15100 0.331284225412680.0497 r16=16100 0.281591591600780.0451 r17=17100 0.236536936944660.0402 r18=18100 0.196325657664060.0353 r19=19100 0.160987039284530.0306 r20=20100 0.130399501820470.0261 r21=21100 0.104319601456380.0219 r22=22100 0.0824124851505380.0181 r23=23100 0.064281738417420.0148 r24=24100 0.0494969385814130.0119 r25=25100 0.0376176733218740.0094 r26=26100 0.0282132549914050.0073 r27=27100 0.020877808693640.0056 r28=28100 0.0152408003463570.0043 r29=29100 0.0109733762493770.0032 r30=30100 0.00779109713705780.0023 r31=31100 0.00545376799594050.0017 r32=32100 0.00376309991719890.0012 r33=33100 0.00255890794369530.0008 r34=34100 0.00171446832227580.0006 r35=35100 0.0011315490927020.0004 r36=36100 0.000735506910256330.0003 r37=37100 0.000470724422564050.0002 r38=38100 0.000296556386215350.0001 r39=39100 0.000183864959453520.0001 r40=40100 0.000112157625266654.4863105 r41=41100 6.72945751599881052.7591105 r42=42100 3.97037993443931051.6676105 r43=43100 2.30282036197481059.9021106 r44=44100 1.31260760632561055.7755106 r45=45100 7.35060259542351063.3078106 r46=46100 4.04283142748291061.8597106 r47=47100 2.18312897084081061.0261106 r48=48100 1.15705835454561065.5539107 r49=49100 6.01670344363721072.9482107 r50=50100 3.0685187562551071.5343107 r51=51100 1.53425937812751077.8247108 r52=52100 7.51787095282471083.9093108 r53=53100 3.60857805735581081.9125108 r54=54100 1.69603168695721089.1586109 r55=55100 7.80174576000331094.291109 r56=56100 3.51078559200151091.966109 r57=57100 1.54474566048071098.80511010 r58=58100 6.642406340066810103.85261010 r59=59100 2.789810662828110101.6461010 r60=60100 1.143822371759510106.86291011 r61=61100 4.57528948703810112.79091011 r62=62100 1.784362899944810111.10631011 r63=63100 6.780579019790410124.27181012 r64=64100 2.508814237322410121.60561012 r65=65100 9.031731254360810135.87061013 r66=66100 3.161105939026310132.08631013 r67=67100 1.074776019268910137.2011014 r68=68100 3.546760863587510142.41181014 r69=69100 1.13496347634810147.83121015 r70=70100 3.518386776678810152.46291015 r71=71100 1.055516033003610157.49421016 r72=72100 3.060996495710510162.20391016 r73=73100 8.570790187989510176.25671017 r74=74100 2.314113350757210171.71241017 r75=75100 6.016694711968610184.51251018 r76=76100 1.504173677992210181.14321018 r77=77100 3.610016827181210192.77971019 r78=78100 8.303038702516710206.47641020 r79=79100 1.826668514553710201.44311020 r80=80100 3.836003880562710213.06881021 r81=81100 7.672007761125410226.21431022 r82=82100 1.457681474613810221.19531022 r83=83100 2.623826654304910232.17781023 r84=84100 4.460505312318310243.74681024 r85=85100 7.136808499709310256.06631025 r86=86100 1.070521274956410259.20651026 r87=87100 1.49872978493910261.30391026 r88=88100 1.948348720420610271.71451027 r89=89100 2.338018464504810282.08081028 r90=90100 2.571820310955310292.31461029 r91=91100 2.571820310955310302.34041030 r92=92100 2.314638279859710312.12951031 r93=93100 1.851710623887810321.72211032 r94=94100 1.296197436721410331.21841033 r95=95100 7.777184620328710357.38831035 r96=96100 3.888592310164310363.7331036 r97=97100 1.555436924065710371.50881037 r98=98100 4.666310772197210394.5731039 r99=99100 9.332621544394410419.23931041 r100=100100 9.332621544394510439.33261043 r10>r r10max n=10=10



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



Showing 1 comment:
#
Dr Math
Perhaps a more elegant solution: The Kth person gets 99! / (99 - (k-1)! * K / 100exp (k). K + 1. The person gets 99! / (99 - k)! * (K + 1) / 100exp (k + 1) The ratio m (k + 1) / m (k) must be greater than one, ie: the next person in the order will receive a larger portion than the previous one.Applies to k = 1, 2, … 9. The 10th person gets the largest portion.

avatar









Tips to related online calculators
Need help to calculate sum, simplify or multiply fractions? Try our fraction calculator.
Our percentage calculator will help you quickly calculate various typical tasks with percentages.

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Acid solution
    h2so4 By adding 250 grams of a 96% sulfuric acid solution to its 3% solution, we changed its initial concentration to 25%. How many grams of 3% of the acid was used for dilution?
  • Geography tests
    test On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
  • Percentages above 100%
    cmelak What is 122% of 185? What is the meaning of percentages above 100%?
  • Grams
    chemia How many grams of 5% solution do we need to add to 100g of 50% solution to get a 20% solution?
  • Diameters of circles
    circle5 How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
  • Three shapes
    three_bodies 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
  • Disinfecting solution
    desinfect How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
  • Solutions
    bilde How much 60% solution and how much 35% solution is needed to create 100 l of 40% solution?
  • Percents from percent
    percent How much is 13% of 20% of 500 greater than 8% of 14% of 200?
  • Percent change
    rectangles If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
  • Bronze, tin and copper
    zvon Bronze is an alloy of tin and copper. An alloy of 10% tin and 90% copper is Gunmetal. If it contains 20% tin and 80% copper, it is bell metal. How many tons of molten bell metal and how many tons of copper is needed to make 100 tons of Gunmetal?
  • Solution
    chemia What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture?
  • Unknown integer
    cross Find the smallest integer: divided by 2, the remainder is 1. divided by 3, the remainder is 2. divided by 4, the remainder is 3. ... divided by eight, the remainder is 7, divided by 9 the remainder is 8.
  • Hydrochloric acid
    hcl Determine the concentration of which must have a solution of hydrochloric acid that mixing 10 l of the solution with 8 liters of 26% solution to get the solution with a concentration of 50%?
  • Three figures - numbers
    numbers34 The sum of three numbers, if each is 10% larger than the previous one, is 662. Determine the figures.
  • Persons
    ball1 Persons surveyed:100 with result: Volleyball=15% Baseball=9% Sepak Takraw=8% Pingpong=8% Basketball=60% Find the average how many like Basketball and Volleyball. Please show your solution.
  • Divisibility
    dots Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.