ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Solving Mixture Problems

Updated on August 6, 2018

Solving Mixture Problems


One of important and interesting applications of Algebraic equations is found in solving mixture problems. I find solving mixture problems challenging but a little bit confusing. In this hub I presented several mixture problems with their solutions. Hope you will enjoy reading this hub.


Problem Number One :


How many gallons of a liquid that is 74 percent alcohol must be combined with 5 gallons of another liquid that is 90 percent alcohol to obtain a mixture that is 84 percent alcohol ?


Solution :

Let X = The number in gallons of the first liquid

First Liquid :

Number of gallons : X

Percent of Alcohol : 74%

Number of gallons of alcohol : 0 .74X

Second Liquid :

Number of gallons : 5 gallons

Percent of Alcohol : 90%

Number of gallons of Alcohol : (.90)(5) = 4.5 gallons

Mixture:

Number of gallons : X + 5

Percent of Alcohol : 84%

Nunber of gallons of alcohol : 0.84(X + 5)

Working Equation :

The number of gallons of alcohol in the first liquid + The number of gallons of alcohol in the second liquid = The number of gallons of alcohol in the mixture.

0.74 X + 4.5 = 0.84 (X + 5)

0.74X + 4.5 = 0.84X + 4.2

0.74X - 0.84X = 4.2 - 4.5

-0.10 X = -0.3

10X = 30

1/10(10X) = 30 (1/10)

X = 3

Hence the required amount of first liquid is 3 gallons.


Problem Number Two :


A contractor mixed two batches of concrete that were 9.3 percent and 11.3 percent cement to obtain 4,500 lbs of concrete that was 10.8 percent cement. How many pounds of each type of concrete was used ?



Solution :

Let X = pounds of concrete with with 9.3% cement

4,500 – X = pounds of concrete with 11.3 % cement

First Concrete :

Amount in pounds : X

Percent of Cement : 9.3%

Number of pounds cement : 0.093X

Second Concrete:

Amount in pounds : 4,500 – X

Percent of Cement : 11.3%

Number of pound cement : (0.113)(4,500 – X)

Mixture

Amount in pounds: 4,500

Percent of Cement : 10.8%

Amount of cement in pounds : 0.108(4,500) = 486 pounds

Working Equation :

The amount in pounds of cement in concrete one + The amount in pound of cement in concrete two = Amount in pounds of cement in the mixture.

0.093X + 0.113(4,500 – X ) = 486

0.093X + 508.5 – 0.113X = 486

0.093X - 0.113X = 486 - 508.5

- 0.02 X = -22.5

2X = 2250

½(2X) = 2250(1/2)

X = 1,125 lbs

4500 - X = 3,375 lbs.

There were 1125 lbs of concrete with 9.3 % cement while 3375 lbs with 11.3% cement used.


Problem Number Three:


British Sterling is 7.5 percent copper by weight. How many grams of silver must be mixed with 159 grams of an alloy that is 10 percent copper in order to make sterling?


Solution :

Let X = Number of grams of silver that must be mixed with the alloy

Alloy :

Number of grams : 150 grams

Percent Copper : 10%

Amount of Copper in grams : (0.10) (150) = 15 grams

Silver :

Number of grams : X

Percent Copper : 0%

Amount of Copper : 0

Sterling :

Number of grams : 150 + X

Percent Coppet: 7.5%

Amount of Copper : 0.075 ( 150 + X )

Working Equations :

Grams of Copper in Alloy = Grams of Copper in Sterling

15 = 0.075(150 + X )

15 = 11.25 + 0.075 X

15 - 11.25 = 0.075 X

3.75 = 0.075 X

375 = 7.5 X

(1/7.5) 375 = 7.5 X ( 1/7.5)

X = 50 grams

50 grams of silver must be mixed with 150 grams of alloy which is 10% copper in order to make a sterling.

SOURCE :

COLLEGE ALGEBRA By

Rees

Sparks

Rees

Comments

    0 of 8192 characters used
    Post Comment

    • profile image

      susie 

      6 years ago

      thanks a lot

    • profile image

      JHEM 

      7 years ago

      AMAZING

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      8 years ago from Manila

      HI Dave Mathews thanks for gracing this hub. your visit is much appreciated. Blessings and regards.

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      8 years ago from Manila

      HI frogfish thank you for dropping by. Your visit is much appreciated. Blessings to you and regards.

    • Dave Mathews profile image

      Dave Mathews 

      8 years ago from NORTH YORK,ONTARIO,CANADA

      Ate Cristina: even with a Bsc i computers I never could solve one if thos problems. I always got lost with the value "X" in roman numerals "X" = 10

      Brother Dave.

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      8 years ago from Manila

      Hi Cmerritt it is great to hear from you. Thank you for dropping by and appreciating this hub. Your visit and comment is much appreciated. Blessings to you and regards.

    • frogyfish profile image

      frogyfish 

      8 years ago from Central United States of America

      OK, I skimmed through this - knowing I could come back and use your 'formula' when needed. I struggle with those kinds of problems' and always have but SOMETIMES I come up with a right answer - I think! :-) Wow, and thank you!

    • CMerritt profile image

      Chris Merritt 

      8 years ago from Pendleton, Indiana

      Okay, my brain hurts!!! but, I am amazed at those who can accomplish these mathamaical tasks with ease. I CAN, but only with some Tylenol in hand.

      :)

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      8 years ago from Manila

      Hi RevLady thank you for appreciating this hub. Blessings and regards.

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      8 years ago from Manila

      Hi lifegate thank you for dropping by. Your visit and comment is much appreciated. Blessings and regards.

    • RevLady profile image

      RevLady 

      8 years ago from Lantana, Florida

      Like LG said, you have an amazing mind for mathematics. I do not, but thanks for sharing.

      Forever His,

    • lifegate profile image

      William Kovacic 

      8 years ago from Pleasant Gap, PA

      You amaze me. My math is terrible. Thanks for sharing.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com 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: https://hubpages.com/privacy-policy#gdpr

    Show Details
    Necessary
    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 googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    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)
    Marketing
    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.
    Statistics
    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)