Ratio Word Problems Worksheets - Free Printable

I'll solve the problem step by step based on the image provided.

First, let me look closely at the image to understand what information is given and what questions need to be answered.

The image shows a survey about students' favorite sports with the following data:
- Volleyball: 660 students
- Baseball: 1728 students
- Soccer: 672 students
- Tennis: 1062 students
- Basketball: 1236 students

There are 5 questions that need to be answered:

1. Find the ratio of students who like baseball to the students who like tennis.
2. What is the ratio of the most preferred game to the least preferred game among the university students?
3. Identify the games preferably liked by university students in the ratio of 5:6.
4. Find the ratio of the least favorite sport to all the other sports.
5. Compare the ratios of students who like basketball to those who prefer soccer.

I'll now solve each question one by one.

Question 1: Ratio of students who like baseball to students who like tennis
Baseball: 1728 students
Tennis: 1062 students
Ratio = 1728:1062
To simplify, I'll divide both numbers by their greatest common divisor (GCD).
GCD of 1728 and 1062 is 6.
1728 ÷ 6 = 288
1062 ÷ 6 = 177
So the simplified ratio is 288:177.
We can simplify further by dividing by 3:
288 ÷ 3 = 96
177 ÷ 3 = 59
Final ratio: 96:59

Question 2: Ratio of most preferred game to least preferred game
Most preferred: Baseball (1728 students)
Least preferred: Volleyball (660 students)
Ratio = 1728:660
GCD of 1728 and 660 is 12.
1728 ÷ 12 = 144
660 ÷ 12 = 55
Final ratio: 144:55

Question 3: Games preferably liked in ratio of 5:6
I need to find which pair of sports has a ratio close to 5:6.
Let me check different combinations:
- Volleyball (660) to Soccer (672): 660:672 = 55:56 (close to 5:6, but not exact)
- Soccer (672) to Volleyball (660): 672:660 = 56:55
- Tennis (1062) to Basketball (1236): 1062:1236 = 177:206
- Basketball (1236) to Tennis (1062): 1236:1062 = 206:177
- Baseball (1728) to Soccer (672): 1728:672 = 36:14 = 18:7
None of these are exactly 5:6, but Volleyball to Soccer (660:672) is very close to 5:6 (which would be 660:792 if we scale 5:6 to match 660).

Actually, let me recalculate more carefully. If we want a ratio of 5:6, we're looking for two numbers where one is 5/6 of the other or vice versa.
Looking at the numbers again:
Volleyball: 660
Soccer: 672
660/672 = 55/56 ≈ 0.982, while 5/6 ≈ 0.833
This isn't 5:6.

Let me check if any combination gives us 5:6:
If we take 5x and 6x, then 5x + 6x = 11x should be the sum of two sports.
Let's try: 660 and 672 - not 5:6
1062 and 1236 - 1062/1236 = 177/206 ≈ 0.859, while 5/6 ≈ 0.833
Close but not exact.

Actually, let me calculate 5:6 exactly:
If we have 5:6, then for every 5 parts of one sport, there are 6 parts of another.
Looking at the numbers, none of them are in exact 5:6 ratio. The closest might be Tennis (1062) and Basketball (1236), but 1062:1236 = 177:206, which is not 5:6.

Wait, let me check if I'm misunderstanding. Maybe they want us to find which two sports have a ratio that simplifies to 5:6.
Let me check all pairs:
- Volleyball:Soccer = 660:672 = 55:56
- Volleyball:Tennis = 660:1062 = 110:177
- Volleyball:Basketball = 660:1236 = 55:103
- Volleyball:Baseball = 660:1728 = 55:144
- Soccer:Tennis = 672:1062 = 112:177
- Soccer:Basketball = 672:1236 = 56:103
- Soccer:Baseball = 672:1728 = 14:36 = 7:18
- Tennis:Basketball = 1062:1236 = 177:206
- Tennis:Baseball = 1062:1728 = 177:288 = 59:96
- Basketball:Baseball = 1236:1728 = 103:144

None of these simplify to 5:6. This might be an error in the problem, or perhaps I need to interpret it differently.

Question 4: Ratio of least favorite sport to all other sports
Least favorite: Volleyball (660 students)
All other sports: Baseball (1728) + Soccer (672) + Tennis (1062) + Basketball (1236) = 4698 students
Ratio = 660:4698
GCD of 660 and 4698 is 6.
660 ÷ 6 = 110
4698 ÷ 6 = 783
Final ratio: 110:783

Question 5: Compare ratios of students who like basketball to those who prefer soccer
Basketball: 1236 students
Soccer: 672 students
Ratio = 1236:672
GCD of 1236 and 672 is 12.
1236 ÷ 12 = 103
672 ÷ 12 = 56
Final ratio: 103:56

Let me summarize my answers:

1. Baseball to Tennis: 96:59
2. Most preferred (Baseball) to least preferred (Volleyball): 144:55
3. Games in ratio 5:6: None of the pairs are in exact 5:6 ratio. The closest is Volleyball to Soccer (660:672 = 55:56), but this is not 5:6.
4. Least favorite (Volleyball) to all others: 110:783
5. Basketball to Soccer: 103:56

For question 3, I think there might be an error in the problem or I'm missing something. Let me double-check if any combination could be interpreted as 5:6.

Actually, let me check if 660:792 would be 5:6 (since 660/5 = 132, and 132*6 = 792). But we don't have a sport with 792 students. The closest is Soccer with 672, which is not 792.

I think for question 3, the answer is that no pair of sports has a ratio of exactly 5:6.

Let me provide the final answers:

1. The ratio of students who like baseball to students who like tennis is 96:59.
2. The ratio of the most preferred game (baseball) to the least preferred game (volleyball) is 144:55.
3. There are no two sports among the given options that have a ratio of exactly 5:6.
4. The ratio of the least favorite sport (volleyball) to all other sports is 110:783.
5. The ratio of students who like basketball to those who prefer soccer is 103:56.