Further Ratio question - clarification

[ctmckoay]

Can you kindly see if I'm right in my approach ? If I'm wrong can you please show me the correct approach.

Q : The ratio of the number of soya beans on Tray D to the number of soya beans on Tray G was 2 : 9. Some time later, Teresa placed another soya bean on Tray G whereas Suzannah placed another 50 soya beans on Tray D; the total number of soya beans on Tray D became 14 more than the total number of soya beans on Tray G. How many soya beans were there on Tray D at first ?

Approach taken : D : G = 2 : 9 .
Hence the ratio difference is 7 = 14 (the difference between total D and total G)
The ratio of 1 = 2 beans which means D : G = 4 beans : 18 beans, added with the 50 beans Suzannah put in, Tray D = 54 green beans ??

Appreciate your help

 

[Denis]

Hint:
D: 2k + 50
G: 9k + 1

 

[Deleted member 4993]

Can you kindly see if I'm right in my approach ? If I'm wrong can you please show me the correct approach.

Q : The ratio of the number of soya beans on Tray D to the number of soya beans on Tray G was 2 : 9. Some time later, Teresa placed another soya bean on Tray G whereas Suzannah placed another 50 soya beans on Tray D; the total number of soya beans on Tray D became 14 more than the total number of soya beans on Tray G. How many soya beans were there on Tray D at first ?

Approach taken : D : G = 2 : 9 .
Hence the ratio difference is 7 = 14 (the difference between total D and total G) <<< This is not correct
The ratio of 1 = 2 beans which means D : G = 4 beans : 18 beans, added with the 50 beans Suzannah put in, Tray D = 54 green beans ??

Appreciate your help

Here

D = initial number of soybeen in tray D

G = initial number of soybeen in tray G

D : G = 2 : 9 ? 9 * D = 2 * G It does not say any thing about (G - D)

G = 9/2 * D ................................ (1)

Later

D[sub:1r3emrk5]1[/sub:1r3emrk5] = number of beans in tray D = D + 50

G[sub:1r3emrk5]1[/sub:1r3emrk5] = number of beans in tray G = G + 1

the total number of soya beans on Tray D became 14 more than the total number of soya beans on Tray G

D[sub:1r3emrk5]1[/sub:1r3emrk5] = G[sub:1r3emrk5]1[/sub:1r3emrk5] + 14

D + 50 = G + 1 + 14 .........................................(2)

Using (1) in (2)

D + 50 = 9/2 * D + 15 ......................................(3)

Now solve (3) for unknown D.