To complete bookshelves, a customer at your store needs to purchase vertical brackets to attach to the wall. The customer wants the shelving to be 9 feet high and 10 feet long. The wall brackets come in 48-inch and 60-inch sections. The 48-inch sections cost $12.95; the 60-inch sections cost $16.95. The brackets should be 1 foot from each end and no more than 24 inches apart. What will be the total cost of the brackets, before tax?
A $89.70
B $119.60
C $129.50
D $149.50
OE $179.40
The Correct Answer and Explanation is:
To determine the total cost of the brackets, let’s break the problem down into manageable steps:
Step 1: Determine the number of brackets needed
The shelving is 10 feet long, and brackets should be placed 1 foot from each end and no more than 24 inches (2 feet) apart.
- From each end, placing a bracket 1 foot in = the first bracket is at 1 ft and the last one is at 9 ft.
- That’s a total distance of 8 feet to cover with evenly spaced brackets no more than 2 feet apart.
Now determine how many additional brackets are needed between the 1-ft and 9-ft points:
Divide the 8-foot span by the maximum allowed spacing:
$$
\frac{8}{2} = 4
$$
So we need 4 brackets between the ones at the ends, plus the 2 end brackets, for a total of:
$$
4 + 2 = 6 brackets
$$
Step 2: Determine the length of each bracket needed
The customer wants the shelving to be 9 feet high, and brackets must reach this full height.
Let’s convert the height to inches:
$$
9 \text{ feet} = 108 \text{ inches}
$$
Now choose bracket sections to add up to 108 inches:
- The 60-inch and 48-inch brackets can be combined: $$
60 + 48 = 108 \text{ inches}
$$
So, each vertical bracket will consist of one 60-inch and one 48-inch section.
Step 3: Calculate total cost
Each bracket requires:
- 1 × 60-inch section @ \$16.95
- 1 × 48-inch section @ \$12.95
So the cost per bracket:
$$
16.95 + 12.95 = 29.90
$$
And for 6 brackets:
$$
6 × 29.90 = 179.40
$$
✅ Correct Answer: OE \$179.40
Summary
- 6 vertical brackets needed
- Each bracket is 108 inches tall (9 ft)
- Each bracket built using one 48″ + one 60″ section
- Total cost: \$179.40 before tax.