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 .
State the ratio as 6 chicken sandwiches to 4 veggie sandwiches: 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, let's find the new number of veggie sandwiches. Initially, there were 3 veggie sandwiches ordered. Mr. Swanson orders 1 more, so the new number of veggie sandwiches is 3 + 1 = 4 .
Calculating New Number of Chicken Sandwiches Next, let's find the new number of chicken sandwiches. Initially, there were 5 chicken sandwiches ordered. Mr. Swanson orders 1 more, so the new number of chicken sandwiches is 5 + 1 = 6 .
Expressing the Ratio Now, we need to find the ratio of chicken sandwiches to veggie sandwiches. The new number of chicken sandwiches is 6, and the new number of veggie sandwiches is 4. So, the ratio is 4 6 .
Simplifying the Ratio and Stating the Answer We can simplify the ratio 4 6 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 . However, the answer choices are in the form of 'a chicken sandwiches to b veggie sandwiches', so we should express the ratio as 6 chicken sandwiches to 4 veggie sandwiches.
Examples
Understanding ratios is very useful in real life. For example, if you are baking a cake and the recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, you can use this ratio to scale the recipe up or down depending on how many servings you want to make. Similarly, ratios are used in cooking, mixing paints, or even calculating distances on a map.
After Mr. Swanson's order, the new number of chicken sandwiches is 6 and veggie sandwiches is 4, resulting in a ratio of 6 chicken sandwiches to 4 veggie sandwiches. Therefore, the answer is 6 chicken sandwiches to 4 veggie sandwiches. The correct choice is (C).
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