Please help!
Economy drapes for a certain size window cost $90. They have shallow pleats,
and the width of the fabric is 2 times the window width. Luxury drapes of the same fabric for the same size window have deeper pleats. The width of the fabric is 3 times the window width. What price should the store manager ask for the luxury drapes?
Cross multiply and solve for x.
90/2 = x/3
Domain Definition
To determine the price of the luxury drapes, we need to consider the difference in fabric width between the economy and luxury drapes.
Let's denote the window width as "W" and the price of the luxury drapes as "P".
The width of the fabric for the economy drapes is 2 times the window width, so it would be 2W.
The width of the fabric for the luxury drapes is 3 times the window width, so it would be 3W.
We know that the economy drapes cost $90. Since the fabric width for the economy drapes is 2W, we can set up a proportion:
(2W) / 90 = 1 / (price per width unit of fabric)
Simplifying this equation, we can cross-multiply:
(2W) * (price per width unit of fabric) = 90 * 1
2W * (price per width unit of fabric) = 90
(price per width unit of fabric) = 90 / (2W)
Now, considering the luxury drapes, we can set up a similar proportion:
(3W) / P = 1 / (price per width unit of fabric)
Substituting the value we found for the price per width unit of fabric in terms of W:
(3W) / P = 1 / (90 / (2W))
Next, we simplify the right side of the equation:
(3W) / P = 1 / (90 / (2W))
(3W) / P = 1 * (2W) / 90
(3W) / P = (2W) / 90
Now, we can cross-multiply:
(3W) * (90) = (2W) * P
270W = 2WP
Finally, we solve for P by dividing both sides by 2W:
P = (270W) / (2W)
P = 135
Therefore, the store manager should ask for a price of $135 for the luxury drapes.