Facebook Page
Twitter
RSS
+ Reply to Thread
Results 1 to 2 of 2

Thread: ACT problem

  1. MHB Apprentice

    Status
    Offline
    Join Date
    Sep 2016
    Posts
    11
    Thanks
    0 times
    Thanked
    4 times
    #1
    Before Joseph paints his house, he pours blue paint into 2 buckets of different sizes. He notices that the volume of the larger bucket is 3 times the volume of the smaller bucket. At the end of the day, Joseph estimates that the larger bucket is 3/4 full and the smaller bucket is 1/3 full/ He decides to pour all of the paint from the smaller bucket into the larger bucket. After that, how full is the larger bucket?

    I know the answer is 31/36, but can someone show me how to set it up?

  2. Pessimist Singularitarian
    MHB Coder
    MHB Math Helper
    MHB Ambassador
    MarkFL's Avatar
    Status
    Online
    Join Date
    Feb 2012
    Location
    St. Augustine, FL.
    Posts
    10,739
    Thanks
    30,828 times
    Thanked
    25,599 times
    Thank/Post
    2.384
    Trophies
    20 Highscores
    Awards
    MHB Statistics Award (2016)  

MHB Calculus Award (2016)  

MHB Pre-University Math Award (2016)  

MHB Model Helper Award (2015)  

MHB Calculus Award (2015)
    #2
    The smaller bucket is 1/3 the size of the larger bucket, and so if the smaller bucket is 1/3 full, it contains 1/9 the capacity of the larger bucket (since 1/3 of 1/3 is 1/9). So, to determine how full the larger bucket would be if the smaller bucket's contents are added, we need to start with what it already has and add 1/9 to that:

    $ \displaystyle F=\frac{3}{4}+\frac{1}{9}$

    Since the two denominators are co-prime (they share no common factors), their LCM is their product and so the LCD is $4\cdot9=36$:

    $ \displaystyle F=\frac{3}{4}\cdot\frac{9}{9}+\frac{1}{9}\cdot\frac{4}{4}=\frac{27}{36}+\frac{4}{36}=\frac{27+4}{36}=\frac{31}{36}$

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Math Help Boards