Peter mixes [tex]4 \frac{1}{4}[/tex] cups of orange juice, [tex]2 \frac{1}{4}[/tex] cups of ginger ale, and [tex]6 \frac{1}{5}[/tex] cups of strawberry lemonade to make some punch. What is the total volume of the punch?

A. [tex]12 \frac{1}{6}[/tex]
B. [tex]12 \frac{3}{11}[/tex]
C. 13.2
D. [tex]12 \frac{1}{4}[/tex]



Answer :

Sure, let's go through the step-by-step solution to find out how much punch Peter has made by mixing different drinks.

1. Convert the mixed fractions to improper fractions:
- For the orange juice:
[tex]\(4 \frac{1}{4} = 4 + \frac{1}{4} = 4.25\)[/tex]
- For the ginger ale:
[tex]\(2 \frac{1}{4} = 2 + \frac{1}{4} = 2.25\)[/tex]
- For the strawberry lemonade:
[tex]\(6 \frac{1}{5} = 6 + \frac{1}{5} = 6.2\)[/tex]

2. Next, add up all these values to find the total amount of punch:
- Total punch = [tex]\(4.25 + 2.25 + 6.2 = 12.7\)[/tex]

The total amount of punch Peter has made is 12.7 cups.

Let's compare this to the options given:
- [tex]\(12 \frac{1}{6}\)[/tex] = approximately 12.1667, not the correct amount
- [tex]\(12 \frac{3}{11}\)[/tex] = approximately 12.2727, not the correct amount
- 132, which is way too high and unrealistic in the context
- [tex]\(12 \frac{1}{4}\)[/tex] = 12.25, which is not the correct amount

Thus, none of the provided options exactly match the amount of punch Peter has made, which is 12.7 cups.