Math Problem Statement

This is a diagram of the stage: 10m x 5.6m

The total width of fabric needs to be the width of the stage front.

Curtain fabric is sold in widths of 1.4 m. Several widths of fabric are sewn together to make the curtains.

The length of the curtains needs to be 5.8 m to allow for hems.

What length of fabric does she need?

Solution

To calculate the total fabric required for the curtains, let's break it down step by step:

  1. Width of the stage front:
    The stage has a width of 10 meters.

  2. Curtain fabric width:
    The fabric is sold in widths of 1.4 meters. To cover the entire width of the stage, you'll need to calculate how many widths of fabric are required:

    Number of widths=Width of the stageWidth of the fabric=101.47.14\text{Number of widths} = \frac{\text{Width of the stage}}{\text{Width of the fabric}} = \frac{10}{1.4} \approx 7.14

    Since you can't use a fraction of a width of fabric, you will need to round this up to the nearest whole number. Thus, you will need 8 widths of fabric.

  3. Length of the curtains:
    The required length of the curtains is 5.8 meters (including allowance for hems).

  4. Total fabric required:
    Each width of fabric needs to be 5.8 meters long, and you need 8 widths of fabric. So the total length of fabric required is:

    Total fabric length=8×5.8=46.4 meters\text{Total fabric length} = 8 \times 5.8 = 46.4 \text{ meters}

Therefore, the total length of fabric she needs to buy is 46.4 meters.

Would you like more details or have any questions?


Here are 5 related questions to expand your understanding:

  1. What if the width of the stage was 12 meters instead of 10 meters?
  2. How would the total fabric length change if the fabric width was 1.2 meters instead of 1.4 meters?
  3. What if you wanted to add extra fabric for pleating or folds?
  4. How would the fabric calculation differ if the stage height changed to 6 meters instead of 5.8 meters?
  5. What if the fabric was sold in different standard lengths, how would you adjust?

Tip: Always account for any extra fabric you might need for pleating or other design details in curtains to avoid a shortage.

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Math Problem Analysis

Mathematical Concepts

Measurement
Rounding
Multiplication

Formulas

Number of fabric widths = Width of the stage / Width of the fabric
Total fabric length = Number of fabric widths * Length of the fabric

Theorems

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Suitable Grade Level

Grades 5-7