Question

Kristin and Jessica each improved their yards by planting grass sod and ornamental grass. They bought theirsupplies from the same store.Kristin spent $95 on 8 sq. ft. of grass sod and 13 bunches of ornamental grass.Jessica spent $54 on 6 sq. ft. of grass sod and 4 bunches of omamental grass.Write and solve a system of equations to find the cost of one sq. ft. of grass sod and the cost of one bunch ofomamental grass.Show your work here:Answer:One sq. ft. of grass sod costs $One bunch of ornamental grass costs $

Answer 1

For this problem, we were given the total values for the purchases of two people, along with the description of the amounts of each item they bought. We need to extract from this description the value of each item.

In order to solve this problem, we need to assign a variable for the price of grass sod and ornamental grass. The first one will be "x", and the second will be "y".

If we multiply the price of each item by the amount that each customer bought, then add the results we should obtain the value of the whole purchase. This is done below:

`\begin{cases}8\cdot x+13\cdot y=95 \\ 6\cdot x+4\cdot y=54\end{cases}`

We will multiply the first equation by 3 and the second one by -4.

`\begin{cases}24\cdot x+39\cdot y=285 \\ -24\cdot x-16\cdot y=-216\end{cases}`

Now we need to add both equations to eliminate one variable.

`\begin{gathered} 24x-24x+39y-16y=285-216 \\ 23y=69 \\ y=(69)/(23) \\ y=3 \end{gathered}`

We can replace the value of "y" on either equation to determine "x". Therefore, we have:

`\begin{gathered} 6\cdot x+4\cdot3=54 \\ 6\cdot x+12=54 \\ 6\cdot x=54-12 \\ 6\cdot x=42 \\ x=(42)/(6)=7 \end{gathered}`

One sq. ft. of grass sod costs $7

One bunch of ornamental grass cost $3