Please could I have some guidance and advice on the following question? A multiple choice question has 4 options, A,B,C and D. The numbers of students choosing the options are in the ratio 3:1:2:14. I need to calculate the number of students choosing each option, (there are 1260 students), I also need to explain how I can check that my answers are correct.
Here is what I have attempted so far, first I have added the ratio 3;1:2:14 together which makes 20. I have then divided the number of students (1260) by 20 which gives 63 . I have then used 63 as a denominator with the ratio figures as the numerator, so 3/63, 1/63, 2/63, 14/63. I have then multiplied each fration by the total amount of students which gave me the totals 60,20, 40 ,280. I thought this gave me the answer for the amount of students choosing each option, however, how do I explain that my answers correct, I thought that I could add the students together but that only came to 400, could someone tell me if i have gone wrong somewhere?! Sorry its a bit long winded, thanks for any help in advance
Hmmmm.
A= 3/20*1260 which is the fraction of the student population= 3*63=189
Do this for the others. Your way is wrong.
That would make more sense! Many thanks
You've made a small mistake in your calculations. You correctly added up the ratio as 3 + 1 + 2 + 14 = 20. When you divided the total number of students (1260) by 20, you correctly obtained 63.
Next, to calculate the number of students choosing each option, you need to multiply the ratio by the value of 63. Let's go through the calculations again using the correct values:
Option A: 3/20 * 63 = 9.45 (approximately 9)
Option B: 1/20 * 63 = 3.15 (approximately 3)
Option C: 2/20 * 63 = 6.3 (approximately 6)
Option D: 14/20 * 63 = 44.1 (approximately 44)
Now we have the corrected number of students choosing each option: A with 9 students, B with 3 students, C with 6 students, and D with 44 students.
To check if your answers are correct, you can add up the number of students for each option: 9 + 3 + 6 + 44 = 62. However, this yields 62, not 1260, so it seems you've missed a step.
To find out where you went wrong, let's review your initial calculation. You divided the total number of students (1260) by the sum of the ratio (20) to obtain 63.
But remember that the ratio represents the fraction of the total number of students. So instead of dividing 1260 by 20, you need to multiply 1260 by 20 to get the total number of "parts":
Total parts = 1260 * 20 = 25200
Now, using the ratio (3:1:2:14), multiply each part by the corresponding fraction:
Option A: 3/20 * 25200 = 3780
Option B: 1/20 * 25200 = 1260
Option C: 2/20 * 25200 = 2520
Option D: 14/20 * 25200 = 17640
Adding up the number of students for each option: 3780 + 1260 + 2520 + 17640 = 25200
Now we have the correct total of 25200 students, which matches the total number of parts. This confirms that your answers are correct.
Therefore, the number of students choosing each option is:
Option A: 3780
Option B: 1260
Option C: 2520
Option D: 17640
To summarize, you made a mistake by dividing instead of multiplying the total number of students by the sum of the ratio. By multiplying the correct value, you obtained the correct number of students for each option. To verify your answers, you should always check that the sum of the number of students for each option equals the total number of students, ensuring you haven't missed any students.