Calculate Blind Prices: Scaling from 40x50 to 120x150 Measurements

Question

The price of 40X50 roller blinds is $182 . What is the price of 120X150 roller blinds?

Video Solution

Solution Steps

00:00 Find the price of the large curtain
00:03 Let's find the similarity ratio
00:09 This is the similarity ratio
00:18 The area ratio equals the similarity ratio squared
00:23 Make sure to square both numerator and denominator
00:33 Multiply the price by the area ratio to find the price
00:47 And this is the solution to the question

Step-by-Step Solution

To determine the price of the 120X150 roller blind, follow these steps:

  • Step 1: Calculate the area of the first roller blind:
    The area of the 40X50 blind is 40×50=2000cm240 \times 50 = 2000 \, \text{cm}^2.
  • Step 2: Calculate the area of the second roller blind:
    The area of the 120X150 blind is 120×150=18000cm2120 \times 150 = 18000 \, \text{cm}^2.
  • Step 3: Set up a proportion based on the two areas and the known price:
    200018000=182Price2 \frac{2000}{18000} = \frac{182}{\text{Price}_2}
  • Step 4: Solve for Price2\text{Price}_2:
    Price2=18000×1822000 \text{Price}_2 = \frac{18000 \times 182}{2000}
  • Price2=32760002000 \text{Price}_2 = \frac{3276000}{2000} Price2=1638 \text{Price}_2 = 1638

Hence, the price of the 120X150 roller blind is \boxed{\1638} \).

Answer

$1638