Flower shop

In a flower shop, a bunch containing 3 tulips, 2 roses, and 1 daffodil cost $10.79. A different bunch containing 1 tulip, 2 roses, and 3 daffodils costs $10.13. A tulip costs 35 cents more than a rose.
How much does 1 tulip and 1 rose, and 1 daffodil cost?

Final Answer:

t =  1.97
r =  1.62
d =  1.64

Step-by-step explanation:

$$\begin{gathered} 3t+2r+1d=10.79 \\ 1t+2r+3d=10.13 \\ t=0.35+r \\ 3\cdot t+2\cdot r+1\cdot d=10.79 \\ 1\cdot t+2\cdot r+3\cdot d=10.13 \\ d+2r+3t=10.79 \\ 3d+2r+t=10.13 \\ r-t=-0.35 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 1.333r+2.667t=7.413 \\ Row3-\frac{1}{1.33333333}\cdot Row2\to Row3 \\ -3t=-5.91 \\ t=\frac{-5.91}{-3}=1.97 \\ r=\frac{7.41333333-2.6666666666667t}{1.33333333}=\frac{7.41333333-2.66666667\cdot 1.97}{1.33333333}=1.62 \\ d=\frac{10.13-2r-t}{3}=\frac{10.13-2\cdot 1.62-1.97}{3}=1.64 \\ d=\frac{41}{25}=1.64 \\ r=\frac{81}{50}=1.62 \\ t=\frac{197}{100}=1.97 \end{gathered}$$

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