Respuesta :
This problem is a set of linear equations, with 2 equations and 2 unknowns.
Let H be the price of hostas and B the price of a bunch of ornamental grass.
Micaela spent $125 on 10 hostas and 1 bunch of ornamental grass.
[tex]10H+1B=125[/tex]Krystal spent $110 on 5 hostas and 10 bunches of ornamental grass.
[tex]5H+10B=110[/tex]We can use substitution to solve this system of equations.
From the first equation we have:
[tex]\begin{gathered} 10H+B=125 \\ B=125-10H \end{gathered}[/tex]We use this value of B and replace it in the second equation:
[tex]\begin{gathered} 5H+10B=110 \\ 5H+10(125-10H)=110 \\ 5H+1250-100H=110 \\ 1250-110=100H-5H \\ 1140=95H \\ H=\frac{1140}{95}=12 \end{gathered}[/tex]Now that we know the value of H, we will use the first equation now to calculate the value of B:
[tex]\begin{gathered} B=125-10H \\ B=125-10(12)=125-120 \\ B=5 \end{gathered}[/tex]The cost of a hosta is $12 and the costa of a bunch of ornamental grass is $5.
