To find the total number of cups of punch that Peter makes, we need to add the amounts of each component: orange juice, ginger ale, and strawberry lemonade.
1. Start with the individual amounts:
- Orange juice: [tex]\( 4 \frac{1}{2} \)[/tex] cups
- Ginger ale: [tex]\( 1 \frac{1}{3} \)[/tex] cups
- Strawberry lemonade: [tex]\( 6 \frac{1}{3} \)[/tex] cups
2. Convert the mixed numbers to improper fractions:
- [tex]\( 4 \frac{1}{2} \)[/tex] can be written as [tex]\( \frac{9}{2} \)[/tex] or in decimal form as 4.5 cups.
- [tex]\( 1 \frac{1}{3} \)[/tex] can be written as [tex]\( \frac{4}{3} \)[/tex] or in decimal form as approximately 1.3333333333333333 cups.
- [tex]\( 6 \frac{1}{3} \)[/tex] can be written as [tex]\( \frac{19}{3} \)[/tex] or in decimal form as approximately 6.333333333333333 cups.
3. Add these amounts together:
- Orange juice: 4.5 cups
- Ginger ale: 1.3333333333333333 cups
- Strawberry lemonade: 6.333333333333333 cups
4. Now calculate the total:
[tex]\[
4.5 + 1.3333333333333333 + 6.333333333333333 = 12.166666666666666
\][/tex]
5. Convert this decimal back to a mixed number, if needed. The decimal 12.166666666666666 is equivalent to:
[tex]\[
12 \frac{1}{6}
\][/tex]
So, the total number of cups of punch that Peter makes is:
[tex]\[ \boxed{12 \frac{1}{6}} \][/tex]
