Question

James and Amy each improved their yards by planting sod and geraniums. They bought their supplies from the same store. James spent $66 on 2 ft of sod and 4 geraniums. Amy spent $55 on 1 ft of sod and 4 geraniums. Find the cost of one ft of sod and the cost of one geranium.

Answer 1

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,

$\begin{cases}2x+4y=66 \\ x+4y=55\end{cases}$

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,

$11+4y=55$

And solve for y. Subtract 11 from both sides,

$\begin{gathered} 11-11+4y=55-11 \\ 4y=44 \end{gathered}$

And divide both sides by 4,

$\begin{gathered} \frac{4y}{4}=\frac{44}{4} \\ \\ y=11 \end{gathered}$

Hence, one geranium costs $11