# 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?

Result

r =  42
t =  105
o =  36
p =  35:12

#### Solution:

$\ \\ r=2/5 \cdot \ t \ \\ =42 \ \\ r=7/6 \cdot \ o \ \\ r+t+o=183 \ \\ \ \\ 5r-2t=0 \ \\ 7o-6r=0 \ \\ o+r+t=183 \ \\ \ \\ o=36 \ \\ r=42 \ \\ t=105 \ \\$
$t=105$
$o=36$

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