ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Some Interesting Math Problems Part Two

Updated on August 7, 2018

Some Interesting Math Problems Part Two

This hub is a sequel to my previously published hub "Some Interesting Math Problems". Here is another five interesting Math problems. Hope you enjoy it.

Problem Number One :

It costs $4.00 to have a shave at Arthur's Barber Shop and it cost $7.00 to have a haircut . One Sunday 14 people went to the shop and three of them had both a haircut and a shave. If Arthur earned $98.00 that day, how many did he shave?

Solution : Let X = number of people who had a haircut only

Y = number of people who had both a haircut and a shave

Z = number of people who had shave only

Since a haircut costs $7, a shave cost $4 and both $11 we have

98 = 7X + 11Y + 4Z equation (1) But Y = 3 and since X + Y + Z = 14, we get X + Z = 11 or X = 11 - Z We plug in the values of Y and X in equation (1) 98 = 7(11 - Z) + 11 (3) + 4Z so 98 = 77 - 7Z + 33 + 4Z Then 98 - 77 - 33 = - 3 Z, we get Z = 4 , the number had a shave only But 3 persons who had a haircut also had a shave so the total number of person who had a shave is 4 + 3 = 7

Problem Number Two :

2 dozens of apples and 4 dozens of mangoes cost 52 dollars. 3 dozens of mangoes and 4 dozens of bananas cost 59 dollars. If apples and bananas cost the same how much does each mango cost ?

Solution :

Since apples and bananas cost the same let their cost denoted b X and the cost of mangoes be Y, So we have (1) 2X + 4Y = 52

(2) 3Y + 4X = 59

From equation (1) we obtain X = (52 - 4Y)/ 2 and substitute this for X in (2) we get 3Y + 4(52 -4Y) (1/2) = 59 therefore 5Y = 45 or Y = 9

A dozen of mangoes cost 9 dollars therefore a piece of mango costs 9/12 = .75 dollars.

Problem Number Three :

Eight teams entered in the first conference of the NBA. If one team plays the other teams once and only once, how many games will be played in the first conference ?

Solution :

Let us say Team 1 is one of those who entered. Team 1 will play the 7 other teams once, so there are seven games, at least. Now team 2 already played Team 1, so it will only have 6 games remaining. Team 3 already played Teams 1 and 2, so it will have 5 more games. Team 4 already played Teams 1, 2 and 3 so it will play 4 more games. By the same reasoning , team 5 will have 3, Team 6 will have 2 and Team 7 will meet Team 8 for the last game. Therefore there are : 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 games in all.

Problem Number Four :

The Incredible Hulk can dig a tunnel 4 days longer than Spiderman can dig one. If they both work togerher , they can dig a tunnel in 4 4/5 days. How fast can Spiderman dig a tunnel ?

Solution : This is a Work Problem

Let X = number of days can spiderman dig a tunnel

X + 4 = number of hays can Incredible Hul dig a tunnel

Working equation : ( 1/X + 1/X + 4 ) 24/5 = 1

( 24/5X + 24/5X + 20 = 1 ) 5X(5X + 20 )

24(5X + 20 ) + 24 (5X ) = 25 X^2 + 100X

120X + 480 + 120X = 25X^2 + 100X

240X + 480 = 25X^2 + 100X

( 25X^2 - 140X - 480 = 0) 1/5 =

5X^2 28X -96 = 0 By facroring we get (5X + 12 ) ( X - 8 ) = 0

=== X - 8 = 0 = X = 8 Answer : 8 days

Problem Number Five :

A deadly epidemic has swept the small planet ZNNX - 8. On the first day 10 died, on the second day 20 died and on the third 40 died. If the progression of mortality continues this way , in how many days will the planet population be wiped out if the population of ZNNX -8 has 20,470 inhabitants. This is a problem involving geometric sequences.

(20,470 = (10 ) 2 ^(n-1) ) 1/10

2047 = 2^(n-1)

Log 2047 = log 2^(n-1)

(Log 2047 = (n - 1) log 2 ) 1/log 2

Log 2047/log 2 = n - 1

3.31/.3 = n - 1

11 = n - 1

N = 12 days.


    0 of 8192 characters used
    Post Comment

    • nikitha p profile image

      nikitha p 

      8 years ago from India

      Interesting hub! I liked it.

    • Adjust profile image


      10 years ago from Earth

      I think that the problem starts because Arthur's Barber Shop is open and on Sundays …


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)