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**ASSIGNMENT INSTRUCTIONS:**

A friend has given you leftover landscaping bricks. You decide to make a garden bed and surround it with bricks. There are 62 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 $125 for additional materials should you need them. Your local home improvement store sells the same bricks for $1.98 per brick. The displayed sides present the number of bricks on each side, where x is the number of bricks.

Assessment Instructions

Show and explain all steps in your responses to the following parts of the assignment using the Algebra concepts discussed within the course. All mathematical steps and explanations must be typed up and 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.

Part 3: Determine the length of each side.

Part 4: Write an inequality that represents how many bricks can be purchased within your budget.

Part 5: Will you be able to make another complete layer of bricks on top and stay within your budget?

**HOW TO WORK ON THIS ASSIGNMENT (EXAMPLE ESSAY / DRAFT)**

In this scenario, we are given 62 bricks that are 8 inches long each. Our goal is to create a garden bed that is slightly more than twice as long as it is wide, using the bricks as the perimeter. We also have a budget of $125 for additional materials.

Part 1: To find the perimeter of the garden bed, we need to add up the lengths of all four sides. Let’s use “P” to represent the perimeter, and “x” to represent the number of bricks on one side. Since there are four sides of equal length, we can write the equation as:

P = 4x

Part 2: We know that there are 62 bricks in total, so if we divide that by 4 (the number of sides), we get the number of bricks used on each side:

62/4 = 15.5

Since we can’t use a fraction of a brick, we’ll round up to 16 bricks per side.

Part 3: We want the garden bed to be slightly more than twice as long as it is wide. Let’s use “l” to represent the length of the garden bed and “w” to represent the width. We can write an equation that says:

l = 2w + a

where “a” is a small additional amount to make the length slightly more than twice the width. We don’t know what “a” is yet, so we’ll leave it as a variable. We know that the perimeter is equal to 4x, so we can substitute 16 (the number of bricks on each side) for “x”:

4(16) = 64 = 2l + 2w + 2a

Simplifying this equation, we get:

32 = l + w + a

Now we can substitute “2w + a” for “l” in the above equation:

32 = 2w + a + w + a

32 = 3w + 2a

Part 4: We have a budget of $125 for additional materials. Let’s use “b” to represent the number of bricks we can buy with this budget. The cost of one brick is $1.98, so we can write an inequality that represents how many bricks we can purchase within our budget:

b <= 125/1.98

Simplifying this inequality, we get:

b <= 63.13

Since we can’t buy a fraction of a brick, we’ll round down to 63 bricks.

Part 5: We used 64 bricks for the perimeter of the garden bed, so we have 62 – 64 = -2 bricks left over. This means we don’t have enough bricks to make another complete layer on top of the first layer. Therefore, we cannot stay within our budget and make another layer of bricks.

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