Answered

Lenita is sewing new curtains. The table below shows the relationship between the number of stitches in a row and the length of the row.




\multicolumn{2}{|c|}{Sewing}

Number of stitches		Length (cm)

5		1

15		3

20		4

30		6






What is the relationship between the number of stitches and the length?


AThe number of stitches is $\frac{1}{5}$ times the length.
BThe number of stitches is $\frac{1}{3}$ times the length.
CThe number of stitches is 3 times the length.

Verified Answer :

  • We identify the variables as the number of stitches \(S\) and length \(L\), with data pairs \((5, 1), (15, 3), (20, 4), (30, 6)\).
  • We test each provided relationship against the data pairs.
  • The equation \(S = 5 \times L\) correctly predicts every given value in the table.
  • The relationship is: \(\boxed{\text{The number of stitches is } 5 \text{ times the length.}}\)

Explanation

  1. Data and Problem Analysis

We are given a table relating the number of stitches (\(S\)) in a row to the length (\(L\)) of that row in centimeters. Our goal is to determine the mathematical relationship between these two variables based on the provided data points:

  • \((S, L) = (5, 1)\)
  • \((S, L) = (15, 3)\)
  • \((S, L) = (20, 4)\)
  • \((S, L) = (30, 6)\)

We need to test which of the suggested relationships correctly models this data.

  1. Testing and Verifying the Relationship

We will evaluate the three given options:

  1. \(S = \frac{1}{5} \times L\)
  2. \(S = \frac{1}{3} \times L\)
  3. \(S = 5 \times L\)

Let's test each one using the first data point, \((S, L) = (5, 1)\):

  • Option 1: \(S = \frac{1}{5} \times 1 = 0.2 eq 5\)
  • Option 2: \(S = \frac{1}{3} \times 1 = 0.33... eq 5\)
  • Option 3: \(S = 5 \times 1 = 5\). This matches!

We now confirm Option 3 for the remaining data points:

  • For \((15, 3)\): \(S = 5 \times 3 = 15\). This matches.
  • For \((20, 4)\): \(S = 5 \times 4 = 20\). This matches.
  • For \((30, 6)\): \(S = 5 \times 6 = 30\). This matches.

Since the equation \(S = 5 \times L\) is consistent with all data points, it is the correct relationship.

  1. Conclusion

The analysis confirms that for every unit of length \(L\), there are exactly \(5\) stitches. Thus, the number of stitches is \(5\) times the length, which is expressed as \(S = 5 \times L\). The correct option is that the number of stitches is \(5\) times the length.

Examples

Understanding proportional relationships is essential in daily tasks like sewing, cooking, or construction. For instance, if you know a recipe requires 5 cups of flour for every 1 cake, you can determine the flour needed for any number of cakes using the relationship \(F = 5 \times C\). Recognizing these patterns allows you to scale resources efficiently and plan projects accurately.

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