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For the grand movie premiere, how many gallons of special drink are needed if the recipe requires [tex]$4 \frac{1}{2}$[/tex] gallons of sparkling soda, 1 gallon of berry extract, [tex]$2 \frac{3}{4}$[/tex] gallons of frosted lemon fizz, and [tex][tex]$\frac{1}{8}$[/tex][/tex] gallon of crushed starfruit?

Select one:

A. [tex]$9 \frac{1}{2}$[/tex] gallons
B. [tex]$8 \frac{3}{8}$[/tex] gallons
C. [tex][tex]$7 \frac{1}{4}$[/tex][/tex] gallons
D. [tex]$10 \frac{1}{2}$[/tex] gallons



Answer :

GinnyAnswer
Let's solve the problem step by step to find out the total amount of special drink needed for the grand movie premiere.

1. Convert mixed numbers to improper fractions if necessary:
- 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. First, convert the mixed numbers into improper fractions:
- [tex]\( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)[/tex]
- [tex]\( 2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \)[/tex]

3. Now, add up all the quantities:
- Sparkling soda: [tex]\( \frac{9}{2} \)[/tex] gallons
- Berry extract: 1 gallon
- Frosted lemon fizz: [tex]\( \frac{11}{4} \)[/tex] gallons
- Crushed starfruit: [tex]\( \frac{1}{8} \)[/tex] gallon

We need to get a common denominator to add these fractions:
- For [tex]\( \frac{9}{2} \)[/tex]: Multiply by 4: [tex]\( \frac{9}{2} \times \frac{4}{4} = \frac{36}{8} \)[/tex]
- For 1 gallon: Multiply by 8: [tex]\( 1 \times \frac{8}{8} = \frac{8}{8} \)[/tex]
- For [tex]\( \frac{11}{4} \)[/tex]: Multiply by 2: [tex]\( \frac{11}{4} \times \frac{2}{2} = \frac{22}{8} \)[/tex]
- For [tex]\( \frac{1}{8} \)[/tex]: Already has the denominator 8

4. Add these fractions:
- [tex]\( \frac{36}{8} + \frac{8}{8} + \frac{22}{8} + \frac{1}{8} \)[/tex]

5. Combine the numerators over the common denominator:
- [tex]\( \frac{36 + 8 + 22 + 1}{8} = \frac{67}{8} \)[/tex]

6. Convert the improper fraction back to a mixed number:
- [tex]\( \frac{67}{8} = 8 \frac{3}{8} \)[/tex]

Thus, the total amount of special drink needed is [tex]\( 8 \frac{3}{8} \)[/tex] gallons.

Therefore, the correct choice is:
[tex]\( 8 \frac{3}{8} \)[/tex] gallons

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