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

Q: Why do I need to calculate areas instead of just using the measurements directly?

Roller blind pricing is based on the total amount of material needed, which is the area. A 120×150 blind uses 9 times more material than a 40×50 blind, so it costs 9 times more!

Q: How do I know which numbers go where in the proportion?

Set it up as $ \frac{\text{Small Area}}{\text{Large Area}} = \frac{\text{Small Price}}{\text{Large Price}} $. Keep the same blind size in the same position (top or bottom) on both sides of the equation.

Q: Can I use a different method instead of proportions?

Yes! Find the price per square unit: $182 ÷ 2000 = $0.091 per cm². Then multiply by the larger area: $0.091 × 18000 = $1638.

Q: How can I check if my proportion is set up correctly?

Cross-multiply and see if it makes sense: smaller area × larger price should equal larger area × smaller price. If 2000 × 1638 = 18000 × 182, you're correct!

Proportional Scaling with Area Calculations

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

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Step-by-step video solution

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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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

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 $40 \times 50 = 2000 \, \text{cm}^2$ .
Step 2: Calculate the area of the second roller blind:
The area of the 120X150 blind is $120 \times 150 = 18000 \, \text{cm}^2$ .
Step 3: Set up a proportion based on the two areas and the known price:
$\frac{2000}{18000} = \frac{182}{\text{Price}_2}$
Step 4: Solve for $\text{Price}_2$ :
$\text{Price}_2 = \frac{18000 \times 182}{2000}$

\text{Price}_2 = \frac{3276000}{2000}

\text{Price}_2 = 1638

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

Final Answer

$1638

Key Points to Remember

Essential concepts to master this topic

Area Formula: Multiply length by width to find total area
Proportion Setup: $\frac{Area_1}{Area_2} = \frac{Price_1}{Price_2}$ where 2000:18000 = 182:Price
Check: Verify 18000 × 182 ÷ 2000 = 1638 by cross-multiplication ✓

Common Mistakes

Avoid these frequent errors

Using linear dimensions instead of areas for pricing
Don't set up proportion as 40:120 = 182:Price = wrong answer of $546! Roller blind pricing depends on total material area, not just one dimension. Always calculate both areas first, then set up your proportion using the complete areas.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to calculate areas instead of just using the measurements directly?

Roller blind pricing is based on the total amount of material needed, which is the area. A 120×150 blind uses 9 times more material than a 40×50 blind, so it costs 9 times more!

How do I know which numbers go where in the proportion?

Set it up as $\frac{\text{Small Area}}{\text{Large Area}} = \frac{\text{Small Price}}{\text{Large Price}}$ . Keep the same blind size in the same position (top or bottom) on both sides of the equation.

Can I use a different method instead of proportions?

Yes! Find the price per square unit: $182 ÷ 2000 = $0.091 per cm². Then multiply by the larger area: $0.091 × 18000 = $1638.

What if I get a decimal answer?

Round to the nearest cent for money problems. However, in this case, the calculation works out to exactly $1638 with no decimals needed.

How can I check if my proportion is set up correctly?

Cross-multiply and see if it makes sense: smaller area × larger price should equal larger area × smaller price. If 2000 × 1638 = 18000 × 182, you're correct!

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