The table shows the sandwich orders from a deli.
\begin{tabular}{|c|c|}\hline Type of Sandwich & Number Ordered \\ \hline Cheese & 6 \\ \hline Veggie & 3 \\ \hline Chicken & 5 \\ \hline\end{tabular}
Suppose Mr. Swanson turns in a late order for 1 veggie sandwich and 1 chicken sandwich. What is the new ratio of chicken sandwiches to veggie sandwiches?
A. 3 chicken sandwiches to 5 veggie sandwiches
B. 4 chicken sandwiches to 4 veggie sandwiches
C. 6 chicken sandwiches to 4 veggie sandwiches
D. 6 chicken sandwiches to 7 veggie sandwiches
Answer (2)
Calculate the new number of veggie sandwiches: 3 + 1 = 4 .
Calculate the new number of chicken sandwiches: 5 + 1 = 6 .
Express the new ratio of chicken sandwiches to veggie sandwiches: 4 6 .
The new ratio of chicken sandwiches to veggie sandwiches is 6 c hi c k e n s an d w i c h es t o 4 v e gg i es an d w i c h es .
Explanation
Understanding the Problem We are given the initial number of cheese, veggie, and chicken sandwiches ordered. Mr. Swanson orders 1 veggie and 1 chicken sandwich. We need to find the new ratio of chicken sandwiches to veggie sandwiches.
Calculating New Number of Veggie Sandwiches First, we calculate the new number of veggie sandwiches. The initial number of veggie sandwiches is 3, and Mr. Swanson orders 1 more. So, the new number of veggie sandwiches is 3 + 1 = 4 .
Calculating New Number of Chicken Sandwiches Next, we calculate the new number of chicken sandwiches. The initial number of chicken sandwiches is 5, and Mr. Swanson orders 1 more. So, the new number of chicken sandwiches is 5 + 1 = 6 .
Expressing the Ratio Now, we express the new ratio of chicken sandwiches to veggie sandwiches. The new number of chicken sandwiches is 6, and the new number of veggie sandwiches is 4. Therefore, the ratio is 4 6 .
Simplifying the Ratio Finally, we simplify the ratio. The fraction 4 6 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, 4 6 = 4 ÷ 2 6 ÷ 2 = 2 3 . The ratio of chicken sandwiches to veggie sandwiches is 6 to 4, which simplifies to 3 to 2. However, the question asks for the ratio of chicken sandwiches to veggie sandwiches, and the options provided are in the form 'x chicken sandwiches to y veggie sandwiches'. So, we should express the ratio as 6 chicken sandwiches to 4 veggie sandwiches.
Examples
Ratios are used in everyday life, such as when cooking. For example, a recipe might call for a ratio of 2 cups of water to 1 cup of rice. If you want to make a larger batch of rice, you need to maintain the same ratio to ensure the rice cooks properly. Understanding ratios helps you scale recipes and maintain the correct proportions.
The new ratio of chicken sandwiches to veggie sandwiches, after adding Mr. Swanson's late order, is 6 to 4. Thus, the correct answer is "6 chicken sandwiches to 4 veggie sandwiches". This corresponds to option C.
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