A friend has given you left-over landscaping bricks. You decide to make a garden bed and surround it with the bricks. There are 86 bricks, and each brick is 8 inches long. You would like the garden bed to be slightly more than twice as long as it is wide, as shown in the diagram below. You have also given yourself a budget of $115 for additional materials should you need them. Your local home improvement store sells the same bricks for $1.25 per brick. The displayed sides present the number of bricks on each side, where x is a number of bricks.
Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.
Part 1: Write an equation representing the perimeter of the garden bed.
Part 2: Calculate how many bricks are used on each side of the garden bed.
Part 3: Determine the length of each side after the bricks are added.
Part 4: Write an inequality that represents how many bricks can be purchased within your budget. Let y represent the number of bricks.
Part 5: Will you be able to make another complete layer of bricks on top and stay within your budget? Hint: your budget is only for the second layer of bricks.