Let's solve each of the ratio word problems step by step.
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1. The ratio of boys to girls in a classroom is 7 to 11. If there are a total of 49 boys in the classroom, then how many boys and girls are there altogether?
- Ratio of boys : girls = 7 : 11
- Number of boys = 49
We can set up a proportion:
$$
\frac{7}{11} = \frac{49}{x}
$$
Where $ x $ is the number of girls.
Cross-multiply:
$$
7x = 11 \times 49 = 539
\Rightarrow x = \frac{539}{7} = 77
$$
So, there are
77 girls.
Total students = boys + girls = $ 49 + 77 = 126 $
✔ Answer: 126 students altogether
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2. The ratio of marbles to stones in a large pot is 6 to 7. If there are 42 marbles, then how many stones are there?
- Ratio marbles : stones = 6 : 7
- Marbles = 42
Set up proportion:
$$
\frac{6}{7} = \frac{42}{x}
$$
Cross-multiply:
$$
6x = 7 \times 42 = 294
\Rightarrow x = \frac{294}{6} = 49
$$
✔ Answer: 49 stones
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3. The ratio of coins to notes in a bag is 3 to 8. If there are a total of 24 coins, then how many notes are there?
- Ratio coins : notes = 3 : 8
- Coins = 24
Set up proportion:
$$
\frac{3}{8} = \frac{24}{x}
$$
Cross-multiply:
$$
3x = 8 \times 24 = 192
\Rightarrow x = \frac{192}{3} = 64
$$
✔ Answer: 64 notes
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4. The ratio of black bags to blue bags is 5 to 3. If there are a total of 10 black bags, then how many blue bags are there?
- Ratio black : blue = 5 : 3
- Black bags = 10
Set up proportion:
$$
\frac{5}{3} = \frac{10}{x}
$$
Cross-multiply:
$$
5x = 3 \times 10 = 30
\Rightarrow x = \frac{30}{5} = 6
$$
✔ Answer: 6 blue bags
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5. The ratio of trucks to cars is 7 to 8. If there are a total of 21 trucks, how many cars are there?
- Ratio trucks : cars = 7 : 8
- Trucks = 21
Set up proportion:
$$
\frac{7}{8} = \frac{21}{x}
$$
Cross-multiply:
$$
7x = 8 \times 21 = 168
\Rightarrow x = \frac{168}{7} = 24
$$
✔ Answer: 24 cars
---
6. The ratio of red ribbons to green ribbons is 4 to 6. If there are a total of 32 red ribbons, then how many green ribbons are there?
- Ratio red : green = 4 : 6 (can simplify to 2:3, but we'll use original)
- Red ribbons = 32
Set up proportion:
$$
\frac{4}{6} = \frac{32}{x}
$$
Cross-multiply:
$$
4x = 6 \times 32 = 192
\Rightarrow x = \frac{192}{4} = 48
$$
✔ Answer: 48 green ribbons
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7. The volume of water in two containers is in the ratio of 6 to 7. If the volume of the first container is 36 liters, find the volume of the second container?
- Ratio container 1 : container 2 = 6 : 7
- Container 1 = 36 liters
Set up proportion:
$$
\frac{6}{7} = \frac{36}{x}
$$
Cross-multiply:
$$
6x = 7 \times 36 = 252
\Rightarrow x = \frac{252}{6} = 42
$$
✔ Answer: 42 liters
---
✔ Final Answers Summary:
1.
126 students
2.
49 stones
3.
64 notes
4.
6 blue bags
5.
24 cars
6.
48 green ribbons
7.
42 liters
Let me know if you'd like these explained with diagrams or visual models!
Parent Tip: Review the logic above to help your child master the concept of ratio word problems with the ratio.
