text: # Question
  
  There were some marbles at a shop. The ratio of the number of red marbles to the number of blue marbles was 2:3. When 50 more red marbles and 30 more blue marbles were added, the ratio of the number of red marbles to the number of blue marbles became 5:6. How many marbles were there at first?
  
  Let the original number of red marbles be x and the number of blue marbles y.
  According to the beginning of the card, we have the following number of marbles: x+50 , y+30.
  We have a system of equations: x/y = 2/3 >> 3x-2y= 0 (1)
  (x+50)/(y+30)=5/6
  >> 6x+300 = 5y + 150
  >> 6x – 5y = -150 (2)
  >From (1) and (2) >> y = 150, x= 100
  
  picos school
  
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  For this question, we will parts and units to solve it.
  
  at first, there will be 2 units for red marbles and 3 units for blue marbles. After 50 red and 30 blue marbles were added, there will be 5 parts of red marbles and 6 parts of blue marbles.
  
  Hennce, the equation will be as such.
  
  2u + 50 = 5p
  
  3u + 30 = 6p
  
  making parts the same,
  
  12u + 300 = 30p
  
  15u + 150 = 30p
  
  hence 12u + 300 = 15u + 150
  
  3u = 150
  
  1u = 50
  
  total marbles will be 50 x 5 = 250
  
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  There were some marbles at a shop. The ratio of the number of red marbles to the number of blue marbles was 2:3. When 50 more red marbles and 30 more blue marbles were added, the ratio of the number of red marbles to the number of blue marbles became 5:6. How many marbles were there at first?=
  
  Total = 5 Units (2 Units Red and 3 Units Blue)
  
  6* (2 Units + 50) = 5 * (3Units + 30)
  
  12 Units + 300 = 15 Units + 150
  
  3 Units = 150
  
  5 Units = 250
  
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  Red : Blue
  = 2: 3
  = 4: 6
  
  After adding, (based on the above ratio)
  Red : Blue
  = 4u+50 : 6u+30
  = 4u+50 : 6(u+5)
  
  The given ratio, after adding is :
  Red : Blue
  = 5:6
  
  Compare blue ratio, 6(u+5) = 6
  hence, red ratio = 5(u+5)
  
  Equate this to the red ratio found earlier.
  
  5(u+5) = 4u+50
  5u+25 = 4u +50
  u = 25
  
  At first ,
  red marbles = 4u = 4 x 25 = 100
  blue marbles = 6u = 6 x 25 = 150
  
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  x: red marbles
  y:blue marbles
  
  x/y=2/3
  (x+50)/(y+30)=5/6
  
  Solving the equation,
  3x=2y
  6x+300=5y+150—–*
  
  if 3x=2y,(here you times 2 for both side right?)
  6x=4y
  
  sub into *
  4y+300=5y+150
  150=y
  y=150
  
  if y=150,
  use this formula u have found jus now
  3x=2y
  3x=2(150)=300
  after that,bring 3 over,hence 300 /3=100.
  x=100
  
  hence red marbles=100
  blue marbles=150
  
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