Question

The school wants to order a new countertop for the teacher’s lounge. The shape of the countertop that they are replacing is shown below.

A countertop can be broken into 2 rectangles. 1 rectangle has a base of 70 inches and height of 20 inches. The other rectangle has a base of 20 inches and height of 30 inches.
If the new countertop costs $0.75 per square inch, what is the price of the replacement countertop?
$1,500
$1,800
$2,000
$2,400

Answer 1

To find the price of the replacement countertop, we need to calculate the total area of both rectangles that form the shape of the countertop, then multiply that area by the cost per square inch.

First, we calculate the area of the first rectangle:
- Base = 70 inches
- Height = 20 inches

\[
\text{Area of rectangle 1} = \text{Base} \times \text{Height} = 70 \, \text{inches} \times 20 \, \text{inches} = 1400 \, \text{square inches}
\]

Next, we calculate the area of the second rectangle:
- Base = 20 inches
- Height = 30 inches

\[
\text{Area of rectangle 2} = \text{Base} \times \text{Height} = 20 \, \text{inches} \times 30 \, \text{inches} = 600 \, \text{square inches}
\]

Now, we sum the areas of both rectangles to get the total area of the countertop:

\[
\text{Total area} = \text{Area of rectangle 1} + \text{Area of rectangle 2} = 1400 \, \text{square inches} + 600 \, \text{square inches} = 2000 \, \text{square inches}
\]

Next, we calculate the cost of the new countertop by multiplying the total area by the cost per square inch:

\[
\text{Cost} = \text{Total area} \times \text{Cost per square inch} = 2000 \, \text{square inches} \times 0.75 \, \text{dollars/square inch} = 1500 \, \text{dollars}
\]

Thus, the price of the replacement countertop is **$1,500**.