Question

6. (10 pts) A rectangular garden has a walkway around it. The area of the garden is 3(2x - 5). The combined area of the garden and the walkway is 7(4x + 3). Find the area of the walkway around the garden as the sum of two terms.

Answer 1

The area of the garden = 3(2x - 5)

The area of the garden and walkway = 7(4x + 3)

Let x = area of the graden

Let y = area of walkway

Since the sum of area of garden and walkway is 7(4x + 3)

Hence, x + y = 7(4x + 3)

Since, area of the garden is 3(2x - 5)

Therefore, x = 3(2x - 5)

Combining the two equations

x + y = 7(4x + 3)

x = 3(2x - 5)

To find the area of walkway, substitute the value of x in the equation 1

3(2x - 5) + y = 7(4x + 3)

Open the parentheses

3*2x - 3*5 + y = 7*