- The Monday ratio of waffle cones to sugar cones is \(\frac{14}{6}\).
- The Tuesday ratio of waffle cones to sugar cones is \(\frac{7}{3}\).
- By simplifying \(\frac{14}{6}\) by a factor of 2, we find \(\frac{14 \div 2}{6 \div 2} = \frac{7}{3}\).
- The correct proportion is \(\boxed{\frac{14}{6} = \frac{7}{3}}\).
Explanation
- Analyze the Given Ratios
To represent the cone sales correctly, we analyze the relationship between waffle cones and sugar cones for both days. On Monday, the ratio of waffle cones to sugar cones is 14 to 6, which can be written as the fraction \(\frac{14}{6}\). On Tuesday, the ratio of waffle cones to sugar cones is 7 to 3, which can be written as the fraction \(\frac{7}{3}\). A proportion is an equation stating that two ratios are equal, so we need to determine if \(\frac{14}{6} = \frac{7}{3}\).
- Compare the Ratios Through Simplification
To check if the two ratios are equivalent, we simplify the fraction representing Monday's sales. The greatest common divisor of 14 and 6 is 2. By dividing both the numerator and the denominator of \(\frac{14}{6}\) by 2, we get:
\[\frac{14 \div 2}{6 \div 2} = \frac{7}{3}.\]
Since this simplified fraction matches the ratio from Tuesday, we conclude that the two ratios are indeed equal.
- Conclusion
Based on our comparison, the proportion that correctly represents the relationship between the cone sales on Monday and Tuesday is \(\frac{14}{6} = \frac{7}{3}\). This confirms that the first option is the correct representation. The final answer is \(\boxed{\frac{14}{6} = \frac{7}{3}}\).
Examples
Proportions are used frequently in daily life for scaling and consistency. For example, if a recipe calls for 2 cups of sugar for every 3 cups of flour, you are maintaining a proportion of \(\frac{2}{3}\). If you decide to double the batch, you will need 4 cups of sugar and 6 cups of flour, resulting in \(\frac{4}{6}\). Because \(\frac{4}{6}\) simplifies to \(\frac{2}{3}\), you have correctly maintained the same taste and consistency as the original recipe!