Question

there were 24 teams at a soccer tournament. in all, 12 teams wore red shirts, 6 teams wore blue shirts, 4 teams wore orange shirts, and 2 teams wore white shirts. match the following ratios to what they describe. description ratio the ratio of teams wearing orange to teams wearing blue 1 : 2 the ratio of teams wearing red to total teams 1 : 12 the ratio of teams wearing white to total teams 2 : 3

Explanation:

Step1: Analyze orange to blue ratio

Teams in orange: 4, teams in blue: 6. Simplify \( \frac{4}{6}=\frac{2}{3} \)? Wait, no, wait: 4:6 simplifies by dividing both by 2: 2:3? Wait, no, the given ratio is 1:2? Wait, no, let's recalculate. Wait, 4 (orange) to 6 (blue): \( \frac{4}{6}=\frac{2}{3} \)? No, wait, 4 and 6 have a GCD of 2. 4÷2=2, 6÷2=3. So 2:3? But the first ratio is 1:2? Wait, maybe I made a mistake. Wait, no, let's check each description:

1. Orange to blue: 4 teams (orange) : 6 teams (blue). Simplify: divide numerator and denominator by 2: 2:3? Wait, no, 4/6 = 2/3, so ratio 2:3? But the first ratio given is 1:2. Wait, maybe I mixed up. Wait, no, let's check the second description: red to total. Red:12, total:24. 12:24 = 1:2. Oh! Wait, I see. Let's do each step:

Step1: Orange to blue ratio

Orange teams: 4, Blue teams: 6. Ratio \( 4:6 \). Simplify by dividing both by 2: \( 2:3 \)? No, wait, 4 and 6: GCD is 2. 4÷2=2, 6÷2=3. So 2:3. But the first ratio is 1:2? Wait, no, maybe I misread. Wait, the first description is "orange to blue", ratio given is 1:2? Wait, no, let's check the third description: white to total. White:2, total:24. 2:24 = 1:12. Ah! There we go. Let's correct:

Step1: Orange to blue

Orange (4) : Blue (6). Simplify: divide by 2 → 2:3. Wait, but the ratio options: 1:2, 1:12, 2:3. So:

• "The ratio of teams wearing orange to teams wearing blue": 4:6 = 2:3 (so matches with 2:3)
• "The ratio of teams wearing red to total teams": Red (12) : Total (24) = 12:24 = 1:2 (matches 1:2)
• "The ratio of teams wearing white to total teams": White (2) : Total (24) = 2:24 = 1:12 (matches 1:12)

Wait, so let's re-express each:

1. Orange to blue: 4:6 = 2:3 (so the ratio 2:3)
2. Red to total: 12:24 = 1:2 (ratio 1:2)
3. White to total: 2:24 = 1:12 (ratio 1:12)

So now match:

• "The ratio of teams wearing orange to teams wearing blue" → 2:3
• "The ratio of teams wearing red to total teams" → 1:2
• "The ratio of teams wearing white to total teams" → 1:12

So the correct matches are:

• Orange to blue: 2:3 (but wait, the ratio given is 2:3? Yes, the third ratio is 2:3. Wait, the table has:

Description | Ratio
--- | ---
The ratio of teams wearing orange to teams wearing blue | 1 : 2
The ratio of teams wearing red to total teams | 1 : 12
The ratio of teams wearing white to total teams | 2 : 3

Wait, no, the user's table is:

Description | Ratio
--- | ---
The ratio of teams wearing orange to teams wearing blue | 1 : 2
The ratio of teams wearing red to total teams | 1 : 12
The ratio of teams wearing white to total teams | 2 : 3

But we need to match the description to the correct ratio. Let's compute each:

1. Orange (4) : Blue (6) → 4/6 = 2/3 → ratio 2:3. So this description matches the ratio 2:3 (the third ratio in the table).

1. Red (12) : Total (24) → 12/24 = 1/2 → ratio 1:2 (the first ratio in the table).

1. White (2) : Total (24) → 2/24 = 1/12 → ratio 1:12 (the second ratio in the table).

So the correct matches are:

• "The ratio of teams wearing orange to teams wearing blue" → 2 : 3 (the third ratio)
• "The ratio of teams wearing red to total teams" → 1 : 2 (the first ratio)
• "The ratio of teams wearing white to total teams" → 1 : 12 (the second ratio)

So to match:

1. Description: "The ratio of teams wearing orange to teams wearing blue" → Ratio: 2 : 3 (the third ratio in the table)
2. Description: "The ratio of teams wearing red to total teams" → Ratio: 1 : 2 (the first ratio in the table)
3. Description: "The ratio of teams wearing white to total teams" → Ratio: 1 : 12 (the second ratio in the table)

Answer:

• The ratio of teams wearing orange to teams wearing blue: \( 2 : 3 \)
• The ratio of teams wearing red to total teams: \( 1 : 2 \)
• The ratio of teams wearing white to total teams: \( 1 : 12 \)

(To present as matches: each description paired with the correct ratio. So:

1. "The ratio of teams wearing orange to teams wearing blue" matches \( 2 : 3 \)
2. "The ratio of teams wearing red to total teams" matches \( 1 : 2 \)
3. "The ratio of teams wearing white to total teams" matches \( 1 : 12 \))