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 answer:

r =  42
t =  105
o =  36
p =  35:12

Step-by-step explanation:

$$\begin{gathered} r=2\mathrm{/}5\cdot t \\ r=7\mathrm{/}6\cdot o \\ r+t+o=183 \\ 5r-2t=0 \\ 7o-6r=0 \\ o+r+t=183 \\ o=36 \\ r=42 \\ t=105 \end{gathered}$$

$t=105=105$

$o=36=36$

$p={\displaystyle \frac{t}{o}}={\displaystyle \frac{105}{36}}={\displaystyle \frac{35}{12}}=2\frac{11}{12}\approx 2.9167=35:12$

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