Question

part ii
sarah wants to know how much it will cost to fix up her air hockey table with dimensions \\(1.75\text{ m}\\) by \\(0.9\text{ m}\\). she needs to fix the boards around the table and fix the sheet on top of the table. the wood for around the boards costs \\(\\$0.75/\text{m}\\) and the metal for the top of the table costs \\(\\$1.65/\text{m}^2\\). the supplies are on sale for \\(25\\%\\) off and there is sales tax of \\(13\\%\\).

steps:

1. draw a sketch of the air hockey table (rectangle) and include the measurements. (2)
2. calculate the perimeter of the air hockey table for the wood. (2)
3. calculate the cost of the wood for the boards, if it costs \\(\\$0.75/\text{m}\\). (2)

Explanation:

⚡ Using what you learned: Understanding Perimeter · area formulas for rectangles and squares

Step 1: Calculate the perimeter for the wood boards

The boards go around the outer edge of the rectangular table. We find the perimeter using the length \(l = 1.75\text{ m}\) and width \(w = 0.9\text{ m}\):

$$ P = 2 \times (l + w) $$

$$ P = 2 \times (1.75 + 0.9) = 2 \times 2.65 = 5.3\text{ m} $$

Step 2: Calculate the cost of the wood

The wood costs \(\$0.75\) per meter:

$$ \text{Wood Cost} = 5.3 \times 0.75 = \$3.975 $$

Step 3: Calculate the area for the metal sheet

The metal sheet covers the top surface of the table. We find the area of the rectangle:

$$ A = l \times w $$

$$ A = 1.75 \times 0.9 = 1.575\text{ m}^2 $$

Step 4: Calculate the cost of the metal sheet

The metal costs \(\$1.65\) per square meter:

$$ \text{Metal Cost} = 1.575 \times 1.65 = \$2.59875 $$

Step 5: Find the total cost before discount

Combine the costs of the wood and the metal:

$$ \text{Subtotal} = 3.975 + 2.59875 = \$6.57375 $$

Step 6: Apply the 25% discount

A discount of \(25\%\) means Sarah pays \(75\%\) of the original price:

$$ \text{Discounted Price} = 6.57375 \times (1 - 0.25) = 6.57375 \times 0.75 \approx \$4.93031 $$

Step 7: Apply the 13% sales tax

Add the \(13\%\) sales tax to the discounted price:

$$ \text{Total Cost} = 4.93031 \times (1 + 0.13) = 4.93031 \times 1.13 \approx \$5.57125 $$

Rounding to the nearest cent gives \(\$5.57\).

Answer:

1. Sketch: A rectangle with length \(1.75\text{ m}\) and width \(0.9\text{ m}\).
2. Perimeter: \(5.3\text{ m}\)
3. Cost of wood: \(\$3.98\) (or \(\$3.975\) before rounding)
4. Total cost to fix up the table (including 25% off and 13% tax): \(\$5.57\)