To determine the total number of cups of punch that Peter makes, we need to add up the individual amounts of each ingredient.
First, let’s convert the mixed numbers to improper fractions for ease of calculation:
1. Orange juice:
[tex]\( 4 \frac{1}{4} = 4 + \frac{1}{4} = 4.25 \)[/tex]
2. Ginger ale:
[tex]\( 2 \frac{1}{4} = 2 + \frac{1}{4} = 2.25 \)[/tex]
3. Strawberry lemonade:
[tex]\( 6 \frac{1}{3} = 6 + \frac{1}{3} \approx 6.333333333333333 \)[/tex]
Next, add these amounts together to find the total volume of the punch:
[tex]\[
4.25 + 2.25 + 6.333333333333333 = 12.833333333333332
\][/tex]
Now, we need to compare this result with the given choices to find the correct one:
1. [tex]\( 12 \frac{2}{5} = 12 + \frac{2}{5} = 12.4 \)[/tex]
2. [tex]\( 12 \frac{1}{4} = 12 + \frac{1}{4} = 12.25 \)[/tex]
3. [tex]\( 12 \frac{3}{11} = 12 + \frac{3}{11} \approx 12.272727272727273 \)[/tex]
4. [tex]\( 12 \frac{5}{6} = 12 + \frac{5}{6} \approx 12.833333333333334 \)[/tex]
The result [tex]\( 12.833333333333332 \)[/tex] is closest to [tex]\( 12 \frac{5}{6} \approx 12.833333333333334 \)[/tex].
Therefore, the total number of cups of punch that Peter makes is:
[tex]\[
12 \frac{5}{6}
\][/tex]
