Flowers 2

Cha cruz has a garden. The ratio roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha cruz wonders what the ratio of tulips to orchids is. If Cha cruz has 183 plants, how many of each kind are there?

Correct result:

r =  42
t =  105
o =  36
p =  35:12

Solution:

 r=2/5⋅ t=42 r=7/6⋅ o r+t+o=183  5r−2t=0 7o−6r=0 o+r+t=183  o=36 r=42 t=105 \ \\ r=2/5 \cdot \ t=42 \ \\ r=7/6 \cdot \ o \ \\ r+t+o=183 \ \\ \ \\ 5r-2t=0 \ \\ 7o-6r=0 \ \\ o+r+t=183 \ \\ \ \\ o=36 \ \\ r=42 \ \\ t=105
t=105
o=36
p=to=10536=3512≈2.9167=35:12p=\dfrac{ t }{ o }=\dfrac{ 105 }{ 36 }=\dfrac{ 35 }{ 12 }≈ 2.9167=35:12

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