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Answer :
Sure! Let's solve each problem step by step. Here's how you can work through them:
1. Gorgon's Gaze:
- The Gorgon's gaze affects 3 out of every 8 creatures. If the Gorgon encounters 64 creatures, we need to find out how many creatures are not affected.
- First, calculate the number of affected creatures:
[tex]\[
\text{Affected creatures} = \frac{3}{8} \times 64 = 24
\][/tex]
- Then, find the number of creatures not affected by subtracting the affected ones from the total:
[tex]\[
\text{Not affected} = 64 - 24 = 40
\][/tex]
2. Monster Marathon:
- The ratio of mummies to zombies is 2:7. If there are 63 zombies, how many mummies are there?
- Use the ratio to determine the number of mummies:
[tex]\[
\text{Number of mummies} = \frac{2}{7} \times 63 = 18
\][/tex]
3. Monster Army:
- The ratio of ogres to trolls to goblins is 3:4:5. If there are 48 goblins, how many ogres and trolls are there in total?
- First, find the total parts in the ratio:
[tex]\[
3 + 4 + 5 = 12
\][/tex]
- Find the value of one part using the goblins count:
[tex]\[
\text{One part} = \frac{48}{5} = 9.6
\][/tex]
- Calculate ogres and trolls:
- Ogres: [tex]\(3 \times 9.6 = 28.8\)[/tex]
- Trolls: [tex]\(4 \times 9.6 = 38.4\)[/tex]
- Total ogres and trolls:
[tex]\[
28.8 + 38.4 = 67.2
\][/tex]
4. Creature Appetite:
- A monster consumes 5 humans every day. How many humans will it consume in 2 weeks?
- Calculate total consumption:
[tex]\[
5 \times 14 = 70
\][/tex]
5. Monster Heights:
- The ratio of Frankenstein's height to the Mummy's height is 3:5. If the Mummy is 75 inches tall, how tall is Frankenstein?
- Calculate Frankenstein's height:
[tex]\[
\frac{3}{5} \times 75 = 45
\][/tex]
6. Monster Eggs:
- The ratio of hatched eggs to unhatched eggs is 2:9. If there are 45 unhatched eggs, how many eggs have hatched?
- Calculate hatched eggs:
[tex]\[
\frac{2}{9} \times 45 = 10
\][/tex]
These are the detailed step-by-step solutions to each part of the problem.
1. Gorgon's Gaze:
- The Gorgon's gaze affects 3 out of every 8 creatures. If the Gorgon encounters 64 creatures, we need to find out how many creatures are not affected.
- First, calculate the number of affected creatures:
[tex]\[
\text{Affected creatures} = \frac{3}{8} \times 64 = 24
\][/tex]
- Then, find the number of creatures not affected by subtracting the affected ones from the total:
[tex]\[
\text{Not affected} = 64 - 24 = 40
\][/tex]
2. Monster Marathon:
- The ratio of mummies to zombies is 2:7. If there are 63 zombies, how many mummies are there?
- Use the ratio to determine the number of mummies:
[tex]\[
\text{Number of mummies} = \frac{2}{7} \times 63 = 18
\][/tex]
3. Monster Army:
- The ratio of ogres to trolls to goblins is 3:4:5. If there are 48 goblins, how many ogres and trolls are there in total?
- First, find the total parts in the ratio:
[tex]\[
3 + 4 + 5 = 12
\][/tex]
- Find the value of one part using the goblins count:
[tex]\[
\text{One part} = \frac{48}{5} = 9.6
\][/tex]
- Calculate ogres and trolls:
- Ogres: [tex]\(3 \times 9.6 = 28.8\)[/tex]
- Trolls: [tex]\(4 \times 9.6 = 38.4\)[/tex]
- Total ogres and trolls:
[tex]\[
28.8 + 38.4 = 67.2
\][/tex]
4. Creature Appetite:
- A monster consumes 5 humans every day. How many humans will it consume in 2 weeks?
- Calculate total consumption:
[tex]\[
5 \times 14 = 70
\][/tex]
5. Monster Heights:
- The ratio of Frankenstein's height to the Mummy's height is 3:5. If the Mummy is 75 inches tall, how tall is Frankenstein?
- Calculate Frankenstein's height:
[tex]\[
\frac{3}{5} \times 75 = 45
\][/tex]
6. Monster Eggs:
- The ratio of hatched eggs to unhatched eggs is 2:9. If there are 45 unhatched eggs, how many eggs have hatched?
- Calculate hatched eggs:
[tex]\[
\frac{2}{9} \times 45 = 10
\][/tex]
These are the detailed step-by-step solutions to each part of the problem.
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