Ratio P5

1. There were some flowers at a flower shop. The ratio of the number of roses to the number of tulips was 2:3. When 50 more roses and 30 more tulips were added, the ratio of the number of roses to the number of tulips became 5:6. How many flowers were there at first?

  R          T              6R           5T

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  2    :     3             12      :     15

+50       +30          +300         +150

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  5    :     6             30      :     30

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12 u + 300 --> 15 u + 150

3 u --> 300 – 150 = 150

1 u --> 150 ÷ 3 = 50

5 u --> 5 x 50 = 250 flowers

There were 250 flowers at first.

Alternative method

R        [  4 u ]<   50   >          2 : 3 = 4 : 6. Instead of                

T        [   6 u     ]<  30   >      using 2 and 4 units, use

                                                        4 and 6 units (because of 6 p)

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          [1 u][5]    x    5

R         [        5 p       ] 

T         [          6 p          ]

          [1 u][5]      x       6     Make use of T (before) to

                                          construct T (after)

5 u + 25 --> 4 u + 50          Compare R

1 u --> 50 – 25 = 25

10 u --> 10 x 25 = 250 flowers

There were 250 flowers at first.