3 bouquets of flowers are ordered at the florist. 3 roses 2 carnations and 1 tulip costs $14, 2 carnations and 6 tulips costs $38, and 1 rose 12 carnations and 1 tulip costs $18. How much does each item costs?

The correct answer is : Rose cost is 2.1$,

carnation cost is 0.82$ and

tulip cost is 6.06$

Solution:-

Let rose cost be r$, carnation cost be c$ and tulip cost be t$.

Given 3 roses, 2 carnations and 1 tulip costs 14$.

That is 3r+2c+t = 14, let it be first equation.

Also given 2 carnations and 6 tulips costs 38$.

That is 2c+6t=38

c+3t=19

c=19-3t

Also 1 rose, 12 carnations and 1 tulip costs 18$.

That is r+12c+t=18

Let us plugin c=19-3t in above equation.

r+12 (19-3t) + t = 18

r=35t-210

Let us plugin r and c in first equation.

3 (35t-210) + 2 (19-3t) + t = 14

105t-630+38-6t+t = 14

100t = 606

t=6.06$

c=19-3*6.06 = 0.82$

r=35*6.06-210=2.1$