Answer :
ANSWER
• One foot of sod: $11
,• One geranium: $11
EXPLANATION
First, name the variables:
• x: cost of 1 foot of sod
,• y: cost of 1 geranium
We know that James spent $66 buying 2 feet of sod - which cost 2x, and 4 geraniums - which cost 4y.
Also, Amy spent $55 on 1 ft of sod - with a cost of x, and 4 geraniums - with a cost of 4x.
We have the system of equations,
[tex]\begin{cases}2x+4y=66 \\ x+4y=55\end{cases}[/tex]Solve using elimination - i.e. subtract the second equation from the first,
Hence, one foot of sod costs $11.
To find the cost of one geranium we have to replace x = 11 in one of the equations. Replacing in the second equation,
[tex]11+4y=55[/tex]And solve for y. Subtract 11 from both sides,
[tex]\begin{gathered} 11-11+4y=55-11 \\ 4y=44 \end{gathered}[/tex]And divide both sides by 4,
[tex]\begin{gathered} \frac{4y}{4}=\frac{44}{4} \\ \\ y=11 \end{gathered}[/tex]Hence, one geranium costs $11
The cost of one foot of sod and one geranium from their yard improvements, determined through a system of equations, is $11 each.
James and Amy purchased sod and geraniums for their yard improvements, which allows us to set up a system of equations to find the cost of one ft of sod and one geranium. James spent $66 on 2 ft of sod and 4 geraniums, and Amy spent $55 on 1 ft of sod and 4 geraniums. We can represent the cost of one ft of sod as 's' and the cost of one geranium as 'g'.
This gives us two equations based on their purchases:
2s + 4g = $66 (James' purchase)
1s + 4g = $55 (Amy's purchase)
Subtracting the second equation from the first, we eliminate g and solve for s:
(2s + 4g) - (1s + 4g) = $66 - $55
2s - s = $11
s = $11 (cost of one ft of sod)
Now, we substitute the value of s back into any of the original equations to solve for g:
1s + 4g = $55
1($11) + 4g = $55
$11 + 4g = $55
4g = $44
g = $11 (cost of one geranium)
Therefore, the cost of one ft of sod is $11 and the cost of one geranium is also $11.
