To determine the total quantity of the special drink needed for the grand movie premiere, follow these steps:
1. Identify the quantities of each component in fractions and mixed numbers:
- Sparkling soda: [tex]\(4 \frac{1}{2}\)[/tex] gallons
- Berry extract: 1 gallon
- Frosted lemon fizz: [tex]\(2 \frac{3}{4}\)[/tex] gallons
- Crushed starfruit: [tex]\(\frac{1}{8}\)[/tex] gallon
2. Convert mixed numbers to improper fractions or decimal form:
- [tex]\(4 \frac{1}{2}\)[/tex] gallons can be converted to an improper fraction as [tex]\(\frac{9}{2}\)[/tex] or in decimal form as 4.5 gallons.
- [tex]\(2 \frac{3}{4}\)[/tex] gallons can be converted to an improper fraction as [tex]\(\frac{11}{4}\)[/tex] or in decimal form as 2.75 gallons.
- 1 gallon remains as is.
- [tex]\(\frac{1}{8}\)[/tex] gallon remains as is in fractional form or can be written as 0.125 gallons in decimal form.
3. Sum all the quantities together:
- Add [tex]\(4.5\)[/tex] (sparkling soda) + 1 (berry extract) + 2.75 (frosted lemon fizz) + 0.125 (crushed starfruit).
4. Perform the addition step-by-step:
- First, add the solid numbers and decimals separately:
- [tex]\(4.5 + 1 = 5.5\)[/tex]
- [tex]\(5.5 + 2.75 = 8.25\)[/tex]
- [tex]\(8.25 + 0.125 = 8.375\)[/tex]
5. The total amount of special drink needed is:
[tex]\[8.375\][/tex]
Thus, the total amount of special drink required for the grand movie premiere is 8.375 gallons.
