P5 Maths - Can anyone help?

• Learning is the way

  26 Oct 08, 02:11

  Come across this P5 Maths question and need help here to solve the question.

  A box contained 50-cent coins and 20-cent coins in the ratio of 2:3. Peter took out four 50-cent coins, exchanged them for 20-cents and put the money back into the box. The ratio then became 2:7. Find the sum of money in the box at first.

• skythewood

  26 Oct 08, 02:27

  4 50-cent coin equal to 10 20-cent coin

  treat X, stuff inside bracket() as boxes

   

  before change

  50-cent  X X
  20-cent X X X

  after change

  50-cent  X X                ===> take away 4
  20-cent X X X             ===> add 10

  50-cent  (X-2 )(X-2)
  20-cent  X X X (10)            

  since new ratio is 2:7

  1 unit is equal to (X-2)

  7 unit is (X-2)(X-2)(X-2)(X-2)(X-2)(X-2)(X-2)

  
  

  50-cent  (X-2)(X-2)(X-2)(X-2)(X-2)(X-2)(X-2)
  20-cent  X X X (10)

  
  

  ===>

  
  

  50-cent  X X X X X X X (-14)
  20-cent  X X X (10)

  
  

  ===>

  
  

  50-cent  X X X X (-14)
  20-cent  (10)
  

  ===>

  
  

  50-cent  X X X X 
  20-cent  (10)(14)

  
  

  ===>

  
  

  50-cent  X X X X 
  20-cent  (24)

  ===>

  
  

  50-cent   X  X  X  X 
  20-cent  (6)(6)(6)(6)

  
  

  X = 6

• Learning is the way

  27 Oct 08, 00:05

  Your answer is not correct, but the X-2 idea helps me to derive the answer:

   

  4 50-cent coin equal to 10 20-cent coin

  treat X, stuff inside bracket() as boxes

  before change

  50-cent  (X+2) (X+2)
  20-cent (X+2) (X+2) (X+2)

  after change

  50-cent  X X                  ===> take away 4
  20-cent (X+2) (X+2) (X+2)             ===> add 10

   

  50-cent  (X-2 )(X-2)
  20-cent  X X X (10)            

  since new ratio is 2:7

  
  

  50-cent  (X-2)(X-2)
  20-cent  (X-2) (X-2)(X-2) (10+2+2+2)
• Learning is the way

  27 Oct 08, 00:14

  Oops..sorry ..accidentally clicl "Reply" before completing the solution.

   

  4 50-cent coin equal to 10 20-cent coin

  treat X, stuff inside bracket() as boxes

  before change

  50-cent  (X+2) (X+2)
  20-cent (X+2) (X+2) (X+2)

  after change

  50-cent  X X                                          ===> take away 4
  20-cent (X+2) (X+2) (X+2) +10            ===> add 10

  Rearranging: 

  50-cent  (X)(X)
  20-cent  (X)(X)(X) (10+2+2+2)            

  since new ratio is 2:7

  
  

  50-cent  (X)(X)
  20-cent  (X)(X)(X) (10+2+2+2)   ===> (X)(X)(X)(X)(X)(X)(X)

  4X = 16

    X = 4

  Total value of 50-cent = 8 x $0.50 = $4

  Total value of 20-cent = 28 x $0.20 = $5.60

  Hnece total value of all coins = $9.60
• skythewood

  27 Oct 08, 00:17

  Originally posted by Learning is the way:

  Your answer is not correct, but the X-2 idea helps me to derive the answer:

   

  4 50-cent coin equal to 10 20-cent coin

  treat X, stuff inside bracket() as boxes

  before change

  50-cent  (X+2) (X+2)
  20-cent (X+2) (X+2) (X+2)

  after change

  50-cent  X X                  ===> take away 4
  20-cent (X+2) (X+2) (X+2)             ===> add 10

   

  50-cent  (X-2 )(X-2)
  20-cent  X X X (10)            

  since new ratio is 2:7

  
  

  50-cent  (X-2)(X-2)
  20-cent  (X-2) (X-2)(X-2) (10+2+2+2)

  refering to underlined steps...

  what is that? the 50-cent 2 units have -2... while the 20-cent 3 units have -2.

  so is -4 from top, -6 from bottom?

  not sure what steps i did wrong... so what is the correct answer?

• skythewood

  27 Oct 08, 00:22

  Originally posted by Learning is the way:

  Oops..sorry ..accidentally clicl "Reply" before completing the solution.

   

  4 50-cent coin equal to 10 20-cent coin

  treat X, stuff inside bracket() as boxes

  before change

  50-cent  (X+2) (X+2)
  20-cent (X+2) (X+2) (X+2)

  after change

  50-cent  X X                                          ===> take away 4
  20-cent (X+2) (X+2) (X+2) +10            ===> add 10

  Rearranging: 

  50-cent  (X)(X)
  20-cent  (X)(X)(X) (10+2+2+2)            

  since new ratio is 2:7

  
  

  50-cent  (X)(X)
  20-cent  (X)(X)(X) (10+2+2+2)   ===> (X)(X)(X)(X)(X)(X)(X)

  4X = 16

    X = 4

  Total value of 50-cent = 8 x $0.50 = $4

  Total value of 20-cent = 28 x $0.20 = $5.60

  Hnece total value of all coins = $9.60

  this one make more sense...i believe the question is to find the sum of money at first... so... number of 50-cent according to your units is (x+2)(x+2)... 12.

  number of 20-cent is (x+2)(x+2)(x+2).... 18

  since x=4.

  agree?

• Learning is the way

  27 Oct 08, 00:27

  The sum of money never change...yes..you got it right.

• skythewood

  27 Oct 08, 00:29

  Originally posted by Learning is the way:

  The sum of money never change...yes..you got it right.

  thanks

• skythewood

  27 Oct 08, 00:37

  just in case you didn't realise, the $9.60 is wrong.

• secretliker

  27 Oct 08, 00:42

  If number of 50-cent = 12, number of 20-cent = 18

   

  ratio is 2:3, correct.

   

  After the adding and removing,

   

  50-cent = 8, 20-cent = 22

   

  Ratio is not 2:7

• skythewood

  27 Oct 08, 00:45

  Originally posted by secretliker:

  If number of 50-cent = 12, number of 20-cent = 18

   

  ratio is 2:3, correct.

   

  After the adding and removing,

   

  50-cent = 8, 20-cent = 22

   

  Ratio is not 2:7

  try -4 50-cent

  plus 10 20-cent

• secretliker

  27 Oct 08, 00:51

  I see. All along I thought it's removing 4 50-cents and adding 4 20-cents.

• Learning is the way

  27 Oct 08, 00:55

  Did apply -4 50-cent & +10 20-cent.

  After the adding and removing,

   50-cent = 8 , 20-cent = 28

    ($4)            ,   ($5.60)

  Sum = $9.60                                    

• skythewood

  27 Oct 08, 01:07

  Originally posted by Learning is the way:

  Did apply -4 50-cent & +10 20-cent.

  After the adding and removing,

   50-cent = 8 , 20-cent = 28

    ($4)            ,   ($5.60)

  Sum = $9.60                                    

  Come across this P5 Maths question and need help here to solve the question.

  A box contained 50-cent coins and 20-cent coins in the ratio of 2:3. Peter took out four 50-cent coins, exchanged them for 20-cents and put the money back into the box. The ratio then became 2:7. Find the sum of money in the box at first.

   

• baiyun

  30 Oct 08, 09:29

  Hi, Hope this helps