Flowers 2

Cha cruz has a garden. The ratio of roses to tulips is 2:5, and 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:

$$\begin{gathered} r=2/5\cdot t \\ r=7/6\cdot o \\ r+t+o=183 \\ 5r-2t=0 \\ 7o-6r=0 \\ o+r+t=183 \\ Pivot:Row1\leftrightarrow Row2 \\ 7o-6r=0 \\ 5r-2t=0 \\ o+r+t=183 \\ Row3-\frac{1}{7}\cdot Row1\to Row3 \\ 7o-6r=0 \\ 5r-2t=0 \\ 1.857r+t=183 \\ Row3-\frac{1.85714286}{5}\cdot Row2\to Row3 \\ 7o-6r=0 \\ 5r-2t=0 \\ 1.743t=183 \\ t=\frac{183}{1.74285714}=105 \\ r=\frac{0+2t}{5}=\frac{0+2\cdot 105}{5}=42 \\ o=\frac{0+6r}{7}=\frac{0+6\cdot 42}{7}=36 \\ o=36 \\ r=42 \\ t=105 \end{gathered}$$

$t=105$

$o=36$

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

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