Okay, let's see. The problem is asking for which grade the number of male bus riders is closest to 135% of the number of female bus riders. Hmm. So, first, I need to figure out what 135% of the female bus riders would be for each grade, and then compare that to the number of male bus riders. The grade where these two numbers are closest is the answer.

Wait, but the data given is in percentages. So, for each grade, the percentage of male riders and female riders is provided. There are 300 males and 300 females surveyed in each grade. So, the actual numbers would be 300 multiplied by the percentage for males and females, right?

So, for each grade, I can calculate the number of male bus riders by taking 300 times the percentage, and similarly for female bus riders. Then, for each grade, I need to compute 135% of the female bus riders and see how close that is to the male bus riders.

Let me break it down step by step.

First, let's take the 9th grade. The male percentage is 41.1%, so the number of male riders is 300 * 41.1/100. Similarly, female riders are 300 * 39.4/100. Then, 135% of the female riders would be 1.35 times that number. Then, compare that to the male riders to see how close they are.

Let me make a table for each grade:

Grade | Males % | Females % | Male riders | Female riders | 135% of female | Difference
-----|---------|-----------|------------|---------------|---------------|------------
9th  | 41.1    | 39.4      |            |               |               | 
10th | 34.4    | 33.1      |            |               |               | 
11th | 20.6    | 13.8      |            |               |               | 
12th | 11.6    | 8.6       |            |               |               | 

I need to fill in each of these columns. Let's start with the 9th grade.

For 9th grade:
Male riders: 300 * 41.1/100 = 300 * 0.411 = 123.3
Female riders: 300 * 39.4/100 = 300 * 0.394 = 118.2
135% of female riders: 118.2 * 1.35 = Let's calculate that. 118.2 * 1.35. Hmm. 118 * 1.35 is 118 * 1 + 118 * 0.35 = 118 + 41.3 = 159.3. Then, 0.2 * 1.35 is 0.27, so total 159.3 + 0.27 = 159.57. So, approximately 159.57.

Difference between male riders (123.3) and 135% female riders (159.57). The difference is 159.57 - 123.3 = 36.27. Since we want the closest grade, this is a positive difference, so the male riders are 36.27 less than 135% of female riders.

Next, 10th grade:

Male riders: 300 * 34.4/100 = 300 * 0.344 = 103.2
Female riders: 300 * 33.1/100 = 300 * 0.331 = 99.3
135% of female riders: 99.3 * 1.35. Let's compute that. 99 * 1.35 = 99 + 99*0.35 = 99 + 34.65 = 133.65. Then, 0.3 * 1.35 = 0.405. So total 133.65 + 0.405 = 134.055. Approximately 134.06.

Difference: 103.2 vs 134.06. 134.06 - 103.2 = 30.86. So the difference is 30.86. Larger than the 9th grade's 36.27. So 10th grade is worse.

11th grade:

Male riders: 300 * 20.6/100 = 300 * 0.206 = 61.8
Female riders: 300 * 13.8/100 = 300 * 0.138 = 41.4
135% of female riders: 41.4 * 1.35. Let's compute that. 40 * 1.35 = 54. 1.4 * 1.35 = 1.89. So total 54 + 1.89 = 55.89. So approximately 55.89.

Difference: 61.8 vs 55.89. 61.8 - 55.89 = 5.91. Wait, that's a positive difference, meaning male riders are 5.91 more than 135% female riders. Wait, but the question is asking when the number of male riders is closest to 135% of female riders. So, if male riders are higher, the difference is how much higher. So, for 11th grade, the male riders are 5.91 more than 135% of female riders. So the difference is 5.91.

12th grade:

Male riders: 300 * 11.6/100 = 300 * 0.116 = 34.8
Female riders: 300 * 8.6/100 = 300 * 0.086 = 25.8
135% of female riders: 25.8 * 1.35. Let's compute that. 25 * 1.35 = 33.75. 0.8 * 1.35 = 1.08. So total 33.75 + 1.08 = 34.83. Approximately 34.83.

Difference: 34.8 vs 34.83. That's a very small difference, only 0.03. So the male riders are almost exactly 135% of the female riders here. That's the closest.

Wait, so let's recap:

9th grade: difference 36.27 (male riders are less)
10th grade: difference 30.86 (male riders are less)
11th grade: difference 5.91 (male riders are more)
12th grade: difference 0.03 (male riders are almost equal)

Therefore, the grade where male riders are closest to 135% of female riders is the 12th grade. But wait, in the 11th grade, male riders are 5.91 more than 135% female riders, which is a difference of 5.91. The 12th grade is 0.03 difference. So 0.03 is much smaller than 5.91. So 12th grade is the closest.

But let me double-check my calculations because sometimes when I do arithmetic in my head, I might make a mistake.

Starting with 12th grade:

Female riders: 8.6% of 300 = 25.8. 135% of 25.8.

Calculating 25.8 * 1.35:

First, 25 * 1.35 = 33.75

Then, 0.8 * 1.35 = 1.08

Adding them: 33.75 + 1.08 = 34.83

Male riders: 11.6% of 300 = 34.8

Difference: 34.83 - 34.8 = 0.03. Yes, that's correct.

For 11th grade:

Female riders: 13.8% of 300 = 41.4

135% of 41.4: 41.4 * 1.35

40 * 1.35 = 54

1.4 * 1.35 = 1.89

Total 54 + 1.89 = 55.89

Male riders: 20.6% of 300 = 61.8

Difference: 61.8 - 55.89 = 5.91. Correct.

For 10th grade:

Female riders: 33.1% of 300 = 99.3

135% of 99.3: 99.3 * 1.35

99 * 1.35 = 133.65

0.3 * 1.35 = 0.405

Total 133.65 + 0.405 = 134.055

Male riders: 34.4% of 300 = 103.2

Difference: 134.055 - 103.2 = 30.855. Correct.

9th grade:

Female riders: 39.4% of 300 = 118.2

135% of 118.2: 118.2 * 1.35

100 * 1.35 = 135

18.2 * 1.35: 18 * 1.35 = 24.3; 0.2 * 1.35 = 0.27; total 24.3 + 0.27 = 24.57

Total 135 + 24.57 = 159.57

Male riders: 41.1% of 300 = 123.3

Difference: 159.57 - 123.3 = 36.27. Correct.

So, indeed, the 12th grade has the smallest difference of 0.03. Therefore, the answer should be 12th grade.

But let me check again if I interpreted the question correctly. The question asks, "the number of its male bus riders is closest to 135% of the number of its female bus riders." So, for each grade, compute male riders vs 135% female riders. The grade where male riders are closest to that value. Yes, that's what I did.

Wait, but another way to interpret it could be, for each grade, compute the ratio of male riders to female riders, and see which is closest to 135%. But that's equivalent because if male/female ≈ 135%, then male ≈ 135% female.

Yes, so same result.

Another check: 135% is 1.35 times. So, if male riders are 1.35 times female riders, that's the ratio. So, for each grade, compute (male riders / female riders), and see which is closest to 1.35.

Let's compute the ratios:

9th grade: 123.3 / 118.2 ≈ 1.045

10th grade: 103.2 / 99.3 ≈ 1.04

11th grade: 61.8 / 41.4 ≈ 1.49

12th grade: 34.8 / 25.8 ≈ 1.35

Ah, so in the 12th grade, the ratio is exactly 1.35. Wait, 34.8 divided by 25.8 is exactly 1.35? Let's check.

25.8 * 1.35 = 25.8 * 1 + 25.8 * 0.35 = 25.8 + 8.53 = 34.33. Wait, but male riders are 34.8. Wait, maybe my previous calculation was wrong.

Wait, let's compute 25.8 * 1.35:

25 * 1.35 = 33.75

0.8 * 1.35 = 1.08

Total 33.75 + 1.08 = 34.83

But male riders are 34.8, which is 34.8 vs 34.83. So, the ratio is 34.8 / 25.8 ≈ 1.35. Let's compute 34.8 / 25.8.

Divide numerator and denominator by 6: 34.8 /6 = 5.8; 25.8 /6 = 4.3. So 5.8 /4.3 ≈ 1.3488, which is approximately 1.35. So, the ratio is very close to 1.35.

Therefore, the 12th grade's male riders are almost exactly 135% of female riders. So the answer is 12th grade.

But let me verify once again.

For 12th grade:

Female riders: 25.8

135% of 25.8: 25.8 * 1.35 = 34.83

Male riders: 34.8

Difference: 34.83 - 34.8 = 0.03

So, the male riders are 0.03 less than 135% of female riders. So, the closest.

Therefore, the answer is the 12th grade.
Therefore, the grade where the number of male bus riders is closest to $135\%$ of the number of female bus riders is the 12th grade.
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