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Answer :
Certainly! Let's solve the problem step-by-step:
1. Understand the amount of milk available:
- The bakery has 72 half gallons of milk.
2. Convert half gallons to cups:
- We know that 1 cup = [tex]\(\frac{1}{8}\)[/tex] half gallon. This means 1 half gallon = 8 cups (since [tex]\(\frac{1}{1/8} = 8\)[/tex]).
- Therefore, 72 half gallons = [tex]\(72 \times 8 = 576\)[/tex] cups of milk.
3. Determine the amount of milk needed per cake:
- Each cake requires [tex]\(1 \frac{2}{3}\)[/tex] cups of milk.
- Convert [tex]\(1 \frac{2}{3}\)[/tex] to a fraction: [tex]\(1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}\)[/tex] cups of milk per cake.
4. Calculate the number of cakes that can be made:
- Total cups of milk = 576 cups.
- Cups needed per cake = [tex]\(\frac{5}{3}\)[/tex] cups.
- Number of cakes = [tex]\(\frac{\text{Total cups of milk}}{\text{Cups needed per cake}} = \frac{576}{\frac{5}{3}}\)[/tex].
5. Simplify the division:
- [tex]\(\frac{576}{\frac{5}{3}} = 576 \times \frac{3}{5} = \frac{576 \times 3}{5} = \frac{1728}{5} = 345.6\)[/tex].
So, the bakery can make 345.6 cakes with the available milk. Since you can't make a fraction of a cake in reality, the bakery can make 345 complete cakes if they do not use the remaining milk for partial cakes.
1. Understand the amount of milk available:
- The bakery has 72 half gallons of milk.
2. Convert half gallons to cups:
- We know that 1 cup = [tex]\(\frac{1}{8}\)[/tex] half gallon. This means 1 half gallon = 8 cups (since [tex]\(\frac{1}{1/8} = 8\)[/tex]).
- Therefore, 72 half gallons = [tex]\(72 \times 8 = 576\)[/tex] cups of milk.
3. Determine the amount of milk needed per cake:
- Each cake requires [tex]\(1 \frac{2}{3}\)[/tex] cups of milk.
- Convert [tex]\(1 \frac{2}{3}\)[/tex] to a fraction: [tex]\(1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}\)[/tex] cups of milk per cake.
4. Calculate the number of cakes that can be made:
- Total cups of milk = 576 cups.
- Cups needed per cake = [tex]\(\frac{5}{3}\)[/tex] cups.
- Number of cakes = [tex]\(\frac{\text{Total cups of milk}}{\text{Cups needed per cake}} = \frac{576}{\frac{5}{3}}\)[/tex].
5. Simplify the division:
- [tex]\(\frac{576}{\frac{5}{3}} = 576 \times \frac{3}{5} = \frac{576 \times 3}{5} = \frac{1728}{5} = 345.6\)[/tex].
So, the bakery can make 345.6 cakes with the available milk. Since you can't make a fraction of a cake in reality, the bakery can make 345 complete cakes if they do not use the remaining milk for partial cakes.
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