https://file.aiquickdraw.com/mathbot/file/1730482291312snnjox49.jpg

The problem provides the formula:

\[
C = 2.5I
\]

where \( C \) represents the length in centimeters and \( I \) represents the length in inches. The questions are as follows:

### Part (a)
1. **Use the formula to find the number of centimeters in:**
   - **(i) 6 inches**
   - **(ii) 3 feet (1 foot = 12 inches)**

### Part (b)
**Rearrange the formula to express \( I \) in terms of \( C \).**

### Solutions

#### Part (a)
1. **(i) For 6 inches:**

   Using the formula \( C = 2.5I \), substitute \( I = 6 \):
   \[
   C = 2.5 \times 6 = 15 \, \text{cm}
   \]

2. **(ii) For 3 feet:**

   First, convert feet to inches. Since 1 foot = 12 inches, 3 feet is:
   \[
   3 \times 12 = 36 \, \text{inches}
   \]

   Now, substitute \( I = 36 \) into the formula:
   \[
   C = 2.5 \times 36 = 90 \, \text{cm}
   \]

   So, for 3 feet, \( C = 90 \) cm.

#### Part (b)
To express \( I \) in terms of \( C \), rearrange the formula \( C = 2.5I \) by dividing both sides by 2.5:

\[
I = \frac{C}{2.5}
\]

### Summary
- **(a)(i)** 6 inches = 15 cm
- **(a)(ii)** 3 feet = 90 cm
- **(b)** Formula rearranged: \( I = \frac{C}{2.5} \)

Would you like further details on any of the calculations?

### Follow-Up Questions
1. How would the formula change if 1 inch equaled 2.54 cm instead of 2.5 cm?
2. If the length in centimeters was known to be 50, how many inches would that be?
3. How can we verify if this conversion factor (2.5) is accurate?
4. What would the length in centimeters be for 10 feet using this formula?
5. How would you convert a length directly from meters to inches using a similar formula?

### Tip
Always double-check your unit conversions, especially when switching between feet, inches, and centimeters.

You can use the formula C = 2.5I to obtain an approximate value for converting a length, I, in inches, to a length, C, in centimeters. a) Use the formula to find the number of centimeters in: i) 6 inches ii) 3 feet (1 foot = 12 inches). b) Rearrange the formula to express I in terms of C.

Learn to convert inches to centimeters with the formula C = 2.5I. This problem includes calculating centimeters for given inches and feet, and rearranging the formula to solve for inches. Suitable for middle school students.

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