Question

op...OverviewPlansResourcesFollow-up and reports360" reportsMoreSystems of Equations 2Question 4Micaela and Krystal each improved their yards by planting hostas and ornamental grass. They bought their supplies from the same store. Micaela spent $125 on10 hostas and 1 bunch of ornamental grass. Krystal spent $110 on 5 hostas and 10 bunches of ornamental grass. What is the cost of 1 hosta and the cost of 1bunch of ornamental grass? Give your answer as an ordered pair (hosta cost, grass cost).

Answer 1

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.

`10H+1B=125`

Krystal spent $110 on 5 hostas and 10 bunches of ornamental grass.

`5H+10B=110`

We can use substitution to solve this system of equations.

From the first equation we have:

`\begin{gathered} 10H+B=125 \\ B=125-10H \end{gathered}`

We use this value of B and replace it in the second equation:

`\begin{gathered} 5H+10B=110 \\ 5H+10(125-10H)=110 \\ 5H+1250-100H=110 \\ 1250-110=100H-5H \\ 1140=95H \\ H=(1140)/(95)=12 \end{gathered}`

Now that we know the value of H, we will use the first equation now to calculate the value of B:

`\begin{gathered} B=125-10H \\ B=125-10(12)=125-120 \\ B=5 \end{gathered}`

The cost of a hosta is $12 and the costa of a bunch of ornamental grass is $5.