To determine whether there is a proportional relationship between inches and feet, we need to explore the concept of a proportional relationship. A proportional relationship exists when two quantities maintain a constant ratio.
### Step-by-Step Solution
1. Identify the Quantities:
- We are dealing with two quantities here: inches and feet.
2. Understanding the Conversion:
- We know that there are 12 inches in one foot.
3. Establish the Ratio:
- To find out if there is a proportional relationship, we need to see if the ratio between inches and feet is constant.
- For 1 foot, there are 12 inches. The ratio of inches to feet is therefore:
[tex]\[
\text{Ratio} = \frac{\text{Inches}}{\text{Feet}} = \frac{12 \text{ inches}}{1 \text{ foot}} = 12
\][/tex]
4. Check Consistency:
- This same ratio should hold true for any number of feet.
- For 2 feet:
[tex]\[
\text{Inches} = 2 \text{ feet} \times 12 \text{ inches/foot} = 24 \text{ inches}
\][/tex]
[tex]\[
\text{Ratio} = \frac{24 \text{ inches}}{2 \text{ feet}} = 12
\][/tex]
- For 3 feet:
[tex]\[
\text{Inches} = 3 \text{ feet} \times 12 \text{ inches/foot} = 36 \text{ inches}
\][/tex]
[tex]\[
\text{Ratio} = \frac{36 \text{ inches}}{3 \text{ feet}} = 12
\][/tex]
5. Conclusion:
- The ratio of inches to feet remains constant (12) regardless of the number of feet.
- Therefore, we can confirm that there is indeed a proportional relationship between the amount of inches and feet.
In conclusion, the relationship between inches and feet is proportional because the ratio of inches to feet is always consistent and equal to 12.
