Ratio and Proportions Word Problems Worksheets - Free Printable
Educational worksheet: Ratio and Proportions Word Problems Worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Ratio and Proportions Word Problems Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Ratio and Proportions Word Problems Worksheets
Here is the solution to each of the 10 fictional character ratio word problems, with a clear explanation for each:
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1. Superhero Team:
* Given: Ratio of male to female members = 3:5. There are 36 female members.
* Find: Number of male members.
* Solution:
* The ratio 3:5 means for every 5 female members, there are 3 male members.
* We can set up a proportion: (Male / Female) = 3/5.
* Let M be the number of male members. So, M / 36 = 3 / 5.
* Cross-multiply: 5 * M = 3 * 36
* 5M = 108
* M = 108 / 5
* M = 21.6
* Answer: 21.6 male members. *(Note: This is mathematically correct based on the given ratio and number, though having a fraction of a person is unusual in a real-world context.)*
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2. Potion Mixing:
* Given: Ratio of dragon’s breath to phoenix tears = 2:5. Need 35 parts of potion total.
* Find: Parts of each ingredient.
* Solution:
* The ratio 2:5 means the total parts in the mixture are 2 + 5 = 7 parts.
* Dragon’s breath is 2 out of these 7 parts: (2/7) * 35 = 10 parts.
* Phoenix tears are 5 out of these 7 parts: (5/7) * 35 = 25 parts.
* Answer: 10 parts dragon’s breath and 25 parts phoenix tears.
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3. Wizard’s Spell Book:
* Given: Book has 80 pages. 4 out of every 8 pages contain spells.
* Find: Pages that do NOT have spells.
* Solution:
* "4 out of every 8" means half the pages have spells (4/8 = 1/2).
* So, half the pages do NOT have spells: (1/2) * 80 = 40 pages.
* Alternatively, if 4 out of 8 have spells, then 8 - 4 = 4 out of 8 do not have spells. So, (4/8) * 80 = 40 pages.
* Answer: 40 pages do not have spells.
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4. Elf Village:
* Given: Ratio of elves to gnomes to fairies = 2:3:4. There are 60 fairies.
* Find: Total number of creatures.
* Solution:
* The ratio part for fairies is 4. We know this corresponds to 60 actual fairies.
* So, one "part" of the ratio equals 60 / 4 = 15 creatures.
* Elves = 2 parts = 2 * 15 = 30
* Gnomes = 3 parts = 3 * 15 = 45
* Fairies = 4 parts = 4 * 15 = 60 (given)
* Total = 30 + 45 + 60 = 135
* Answer: 135 creatures in total.
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5. Pirate Treasure:
* Given: Captain takes 3/5 of 150 gold coins. Crew gets the rest.
* Find: Coins for the crew.
* Solution:
* Captain's share: (3/5) * 150 = 90 coins.
* Crew's share: Total - Captain's share = 150 - 90 = 60 coins.
* Alternatively, crew gets 1 - 3/5 = 2/5 of the coins: (2/5) * 150 = 60 coins.
* Answer: 60 coins for the crew.
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6. Alien Planets:
* Given: Ratio of blue aliens to green aliens = 2:7. There are 45 green aliens.
* Find: Number of blue aliens.
* Solution:
* The ratio 2:7 means for every 7 green aliens, there are 2 blue aliens.
* Set up a proportion: Blue / Green = 2 / 7.
* Let B be the number of blue aliens. So, B / 45 = 2 / 7.
* Cross-multiply: 7B = 2 * 45
* 7B = 90
* B = 90 / 7
* B ≈ 12.857
* Answer: Approximately 12.86 blue aliens. *(Again, a fractional alien is mathematically correct but unusual.)*
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7. Time Travelers:
* Given: Ratio of humans to aliens = 3:2. There are 15 aliens.
* Find: Number of humans.
* Solution:
* The ratio 3:2 means for every 2 aliens, there are 3 humans.
* Set up a proportion: Humans / Aliens = 3 / 2.
* Let H be the number of humans. So, H / 15 = 3 / 2.
* Cross-multiply: 2H = 3 * 15
* 2H = 45
* H = 45 / 2
* H = 22.5
* Answer: 22.5 humans. *(Fractional human is mathematically correct.)*
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8. Dragon Eggs:
* Given: A dragon lays 6 eggs per month. Ratio of hatched to unhatched eggs = 1:3.
* Find: Hatched eggs in a year.
* Solution:
* First, find total eggs laid in a year: 6 eggs/month * 12 months = 72 eggs.
* The ratio 1:3 means for every 1 hatched egg, there are 3 unhatched eggs, making a total of 1 + 3 = 4 parts.
* Hatched eggs are 1 out of these 4 parts: (1/4) * 72 = 18 eggs.
* Answer: 18 hatched eggs in a year.
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9. Wizard’s Robes:
* Given: Ratio of blue robes to red robes = 9:15. There are 36 blue robes.
* Find: Number of red robes.
* Solution:
* The ratio 9:15 can be simplified by dividing both by 3: 3:5. (This step isn't necessary but can make calculation easier).
* Set up a proportion: Blue / Red = 9 / 15.
* Let R be the number of red robes. So, 36 / R = 9 / 15.
* Cross-multiply: 9R = 36 * 15
* 9R = 540
* R = 540 / 9
* R = 60
* *(Using the simplified ratio 3:5: 36 / R = 3 / 5 → 3R = 36 * 5 → 3R = 180 → R = 60)*
* Answer: 60 red robes.
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10. Creature Habitat:
* Given: Ratio of unicorns to centaurs to griffins = 4:3:2. There are 24 griffins.
* Find: Total number of unicorns and centaurs.
* Solution:
* The ratio part for griffins is 2. We know this corresponds to 24 actual griffins.
* So, one "part" of the ratio equals 24 / 2 = 12 creatures.
* Unicorns = 4 parts = 4 * 12 = 48
* Centaurs = 3 parts = 3 * 12 = 36
* Total unicorns and centaurs = 48 + 36 = 84
* Answer: 84 unicorns and centaurs in total.
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1. Superhero Team:
* Given: Ratio of male to female members = 3:5. There are 36 female members.
* Find: Number of male members.
* Solution:
* The ratio 3:5 means for every 5 female members, there are 3 male members.
* We can set up a proportion: (Male / Female) = 3/5.
* Let M be the number of male members. So, M / 36 = 3 / 5.
* Cross-multiply: 5 * M = 3 * 36
* 5M = 108
* M = 108 / 5
* M = 21.6
* Answer: 21.6 male members. *(Note: This is mathematically correct based on the given ratio and number, though having a fraction of a person is unusual in a real-world context.)*
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2. Potion Mixing:
* Given: Ratio of dragon’s breath to phoenix tears = 2:5. Need 35 parts of potion total.
* Find: Parts of each ingredient.
* Solution:
* The ratio 2:5 means the total parts in the mixture are 2 + 5 = 7 parts.
* Dragon’s breath is 2 out of these 7 parts: (2/7) * 35 = 10 parts.
* Phoenix tears are 5 out of these 7 parts: (5/7) * 35 = 25 parts.
* Answer: 10 parts dragon’s breath and 25 parts phoenix tears.
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3. Wizard’s Spell Book:
* Given: Book has 80 pages. 4 out of every 8 pages contain spells.
* Find: Pages that do NOT have spells.
* Solution:
* "4 out of every 8" means half the pages have spells (4/8 = 1/2).
* So, half the pages do NOT have spells: (1/2) * 80 = 40 pages.
* Alternatively, if 4 out of 8 have spells, then 8 - 4 = 4 out of 8 do not have spells. So, (4/8) * 80 = 40 pages.
* Answer: 40 pages do not have spells.
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4. Elf Village:
* Given: Ratio of elves to gnomes to fairies = 2:3:4. There are 60 fairies.
* Find: Total number of creatures.
* Solution:
* The ratio part for fairies is 4. We know this corresponds to 60 actual fairies.
* So, one "part" of the ratio equals 60 / 4 = 15 creatures.
* Elves = 2 parts = 2 * 15 = 30
* Gnomes = 3 parts = 3 * 15 = 45
* Fairies = 4 parts = 4 * 15 = 60 (given)
* Total = 30 + 45 + 60 = 135
* Answer: 135 creatures in total.
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5. Pirate Treasure:
* Given: Captain takes 3/5 of 150 gold coins. Crew gets the rest.
* Find: Coins for the crew.
* Solution:
* Captain's share: (3/5) * 150 = 90 coins.
* Crew's share: Total - Captain's share = 150 - 90 = 60 coins.
* Alternatively, crew gets 1 - 3/5 = 2/5 of the coins: (2/5) * 150 = 60 coins.
* Answer: 60 coins for the crew.
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6. Alien Planets:
* Given: Ratio of blue aliens to green aliens = 2:7. There are 45 green aliens.
* Find: Number of blue aliens.
* Solution:
* The ratio 2:7 means for every 7 green aliens, there are 2 blue aliens.
* Set up a proportion: Blue / Green = 2 / 7.
* Let B be the number of blue aliens. So, B / 45 = 2 / 7.
* Cross-multiply: 7B = 2 * 45
* 7B = 90
* B = 90 / 7
* B ≈ 12.857
* Answer: Approximately 12.86 blue aliens. *(Again, a fractional alien is mathematically correct but unusual.)*
---
7. Time Travelers:
* Given: Ratio of humans to aliens = 3:2. There are 15 aliens.
* Find: Number of humans.
* Solution:
* The ratio 3:2 means for every 2 aliens, there are 3 humans.
* Set up a proportion: Humans / Aliens = 3 / 2.
* Let H be the number of humans. So, H / 15 = 3 / 2.
* Cross-multiply: 2H = 3 * 15
* 2H = 45
* H = 45 / 2
* H = 22.5
* Answer: 22.5 humans. *(Fractional human is mathematically correct.)*
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8. Dragon Eggs:
* Given: A dragon lays 6 eggs per month. Ratio of hatched to unhatched eggs = 1:3.
* Find: Hatched eggs in a year.
* Solution:
* First, find total eggs laid in a year: 6 eggs/month * 12 months = 72 eggs.
* The ratio 1:3 means for every 1 hatched egg, there are 3 unhatched eggs, making a total of 1 + 3 = 4 parts.
* Hatched eggs are 1 out of these 4 parts: (1/4) * 72 = 18 eggs.
* Answer: 18 hatched eggs in a year.
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9. Wizard’s Robes:
* Given: Ratio of blue robes to red robes = 9:15. There are 36 blue robes.
* Find: Number of red robes.
* Solution:
* The ratio 9:15 can be simplified by dividing both by 3: 3:5. (This step isn't necessary but can make calculation easier).
* Set up a proportion: Blue / Red = 9 / 15.
* Let R be the number of red robes. So, 36 / R = 9 / 15.
* Cross-multiply: 9R = 36 * 15
* 9R = 540
* R = 540 / 9
* R = 60
* *(Using the simplified ratio 3:5: 36 / R = 3 / 5 → 3R = 36 * 5 → 3R = 180 → R = 60)*
* Answer: 60 red robes.
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10. Creature Habitat:
* Given: Ratio of unicorns to centaurs to griffins = 4:3:2. There are 24 griffins.
* Find: Total number of unicorns and centaurs.
* Solution:
* The ratio part for griffins is 2. We know this corresponds to 24 actual griffins.
* So, one "part" of the ratio equals 24 / 2 = 12 creatures.
* Unicorns = 4 parts = 4 * 12 = 48
* Centaurs = 3 parts = 3 * 12 = 36
* Total unicorns and centaurs = 48 + 36 = 84
* Answer: 84 unicorns and centaurs in total.
Parent Tip: Review the logic above to help your child master the concept of ratio and proportions worksheet.
