P5 Sum, 2Q.

• a1111967

  28 Apr 12, 10:32

  Alwyn, Corriane, Keith and Zavier have a total of 1026 marbles. If Corriane gives away 60 of her marbles, she will have 1/4 of the marbles Alwyn has. If keith buys another 150 marbles, he will have 1/2 the number of marbles Alwyn has. If Zavier doubles what he has,he will have the same number of marbles as Alwyn.  How many marbles does Corriane have at first?

   

  A sum of money was awarded to a group of winners who had participated in a contest. 2/5 of the winners were awarded $512 each. 5/6 of the remaining winners were awarded $1024 each. The remaining 21 winners were awarded $21 505 in all. What was the sum of money awarded to all the winners?

   

• MyPillowTalks

  29 Apr 12, 12:39

  Hello a1111967,

  

  Initially, Corraine, Alwyn, Keith and Zavier have 1026 Marbles in total.

  Since the question involves some transaction of marbles, i shall use the information given.

  If Corraine gave away 60 marbles, she would have 1/4 or what Alwyn has, thus, Corraine - 60 = 1/4 of what Alwyn has, which means 1 Unit for corraine, 4 units for Alwyn.
  Note that the "60" in the model denotes what has been given away by corraine
  

  If keith bought 150 marbles, he would have 1/2 of what Alwyn has, thus, Keith + 150 = 1/2 of what Alwyn has, which means 2 Units for Keith, 4 units for Alwyn(This is because from the previous step, Alwyn has 4 units, and now keith has half of what alwyn has).
  Note that the "150" in the model denotes the amount of marbles bought by keith

  Now if zavier doubles what he has, he would have the same number of marbles as Alwyn. From this statement, we can say that if he DID NOT double his quantity of marbles, he would have half of what alwyn has. Therefore, Zavier has 2 Units -- 1/2 of what alwyn has

  Given all these information, we can see that:
  
  1026 - 60 + 150 = Total of 9 Units

  the - 60 is due of corraine giving away 60 marbles, and +150 comes frome keith buying an additional 150 marbles.

  9 units comes from the model drawing (after the giving away and addition of marbles)

  1026 - 60 + 150 = 9 U
  9U = 1116
  1U = 124
  
  From the model, we can see that Corraine originally has 1Unit + 60 Marbles.
  
  Thus, No. of marbles Corraine have = 124 + 60 = 184 Marbles

• FireIce

  29 Apr 12, 13:23

  Originally posted by a1111967: 

  A sum of money was awarded to a group of winners who had participated in a contest. 2/5 of the winners were awarded $512 each. 5/6 of the remaining winners were awarded $1024 each. The remaining 21 winners were awarded $21 505 in all. What was the sum of money awarded to all the winners?

   

  5/6 x 3/5 = 1/2 (received $1024 each)
  1/6 x 3/5 = 1/10 (received $21505 total)
  
  1/10 => 21 winners
  1/2 = 5/10 => 21 x 5 = 105 winners
  105 x 1024 = -calc yourself-

  2/5 = 4/10 => 4 x 21 = 84 winners
  84 x 512 = -calc yourself-

   

  add up everything