Let's call X the cost of one bunch of roses and Y the cost of one palm.
Then, the first order was for 13 bunches of roses and 4 palms, totaling $487, so:
13X + 4Y = 487
Additionally, the second order was for 6 bunches of roses and 2 palms, totaling $232, so:
6X + 2Y = 232
Then, solving for Y on the first equation, we get:
[tex]\begin{gathered} 13X+4Y=487 \\ 4Y=487-13X \\ Y=\frac{487-13X}{4} \\ Y=\frac{487}{4}-\frac{13}{4}X \\ Y=121.75-3.25X \end{gathered}[/tex]Replacing on the second and solving for X, we get:
[tex]\begin{gathered} 6X+2Y=232 \\ 6X+2(121.75-3.25X)=232 \\ 6X+2\cdot121.75-2\cdot3.25X=232 \\ 6X+243.5-6.5X=232 \\ -0.5X+243.5=232 \\ -0.5X=232-243.5 \\ -0.5X=-11.5 \\ X=\frac{-11.5}{-0.5} \\ X=23 \end{gathered}[/tex]Then, we can replace the value of X and calculated the value of Y as:
[tex]\begin{gathered} Y=121.75-3.25X \\ Y=121.75-3.25\cdot23 \\ Y=121.75-74.75 \\ Y=47 \end{gathered}[/tex]Answer: The cost of one bunch of roses is $23 and the cost of one palm is $47
