Question

Landry is building a rectangular flower garden. He wants the garden to be 3 feet longer than it is wide. He wants to buy a birdbath to put in the flower bed and after adding it he wants to have 35 square feet of space for planting. The cost of the birdbath will be $18 per square foot of the area of its base. He also needs to buy soil to cover the entire flower bed, including the space where the birdbath will be. The soil will cost $5 per square foot. He plans to spend a total of $150 on the soil and the birdbath. If x represents the width of the flower bed and y represents the area of the base of the birdbath, then which of the following systems of equations can be used to determine the length and width of the flower bed and the area of the base of the birdbath?

Answer 1

Answer:

Step-by-step explanation:

To create a system of equations, write an equation to model each condition that must be satisfied in the given situation.

It is given that x represents the width of the flower bed and that y represents the area of the base of the birdbath.

Write an equation to represent the condition regarding the planting area in the flower bed. It is given that there is 35 square feet of planting area. The flower bed is 3 feet longer than the width.

x(x+3) - y = 35

Write an equation to represent the condition regarding the cost of the soil and the birdbath. The question gives that the soil will cost $5 per square foot and the birdbath will cost $18 per square foot of the base.

5x(x+3)+18y=150

Combining both of the equations gives the following system of equations.

x(x+3)-y=35

5x(x+3)+18y=150