Question 6: [数形结合思维] 体育中心有国际标准的羽毛球场地 10 片，现场有 34 人在场地打球 (所有场地均被占满)，进行单打的羽毛球场地有 ( ) 片。
Options: B.2 B.3 C. 7 D. 8---Question 6:
[数形结合思维] 体育中心有国际标准的羽毛球场地 10 片，现场有 34 人在场地打球 (所有场地均被占满)，进行单打的羽毛球场地有 ( ) 片。
Options:
B.2
B.3
C. 7
D. 8
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Let's analyze this badminton court problem. We have 10 courts total with 34 people playing. Singles courts have 2 players each, while doubles courts have 4 players each. We need to find how many courts are used for singles.
Now let's set up our equations. Let s be the number of singles courts and d be the number of doubles courts. Since there are 10 courts total, we have s plus d equals 10. For players, singles courts have 2 players each and doubles courts have 4 players each, giving us 2s plus 4d equals 34.
Let's solve this step by step. From the first equation, we can express d as 10 minus s. Substituting this into the second equation: 2s plus 4 times 10 minus s equals 34. This simplifies to 2s plus 40 minus 4s equals 34. Combining like terms gives us negative 2s equals negative 6. Therefore, s equals 3. So there are 3 singles courts.
Let's verify our solution. If s equals 3, then d equals 7. Checking the total courts: 3 plus 7 equals 10, which matches. Checking the total players: 2 times 3 plus 4 times 7 equals 6 plus 28, which equals 34. This also matches. Therefore, our answer is correct: there are 3 singles courts.
In conclusion, we solved this problem using a system of linear equations. With 10 total courts and 34 players, we found that 3 courts are used for singles and 7 courts are used for doubles. This gives us 6 players on singles courts and 28 players on doubles courts, totaling 34 players. The answer is B, which is 3 singles courts.