Freshman:Sophmore = 5:4
Sophmore:Juniors = 7:8
Juniors:Seniors = 9:7
The total is 2158, what is the amount of each grade?
So far, I got 35:32:224/9 for Freshman:Sophmore:Seniors
I don't know if I'm correct, or what I'm doing. Can you please give me help and explain? thanks so much
done. see previous post
To solve this problem, you can use the concept of proportions. You have been given the ratios between the different grade levels, which will help you find the number of students in each grade level.
Let's start by finding the number of sophomores. We know that the ratio of freshmen to sophomores is 5:4 and the total number of students is 2158. To find the number of sophomores, we can set up the proportion:
5/4 = x/2158
To solve for x (the number of sophomores), we can cross-multiply and then divide:
5 * 2158 = 4x
10790 = 4x
x = 10790/4
x ≈ 2697.5
Since we can't have half a person, we need to round this number to the nearest whole number. Therefore, there are approximately 2698 sophomores.
Now, to find the number of juniors, we'll use a similar approach. The ratio of sophomores to juniors is 7:8. We already know there are 2698 sophomores, so we can set up the proportion:
7/8 = 2698/y
Again, cross-multiplying gives:
7 * y = 8 * 2698
7y = 21584
y ≈ 3083.43
Rounding to the nearest whole number, we find there are approximately 3083 juniors.
Finally, to find the number of seniors, we'll use the last ratio of juniors to seniors, which is 9:7. We have 3083 juniors, so the setup is:
9/7 = 3083/z
Cross-multiplying:
9 * z = 7 * 3083
9z = 21581
z ≈ 2397.89
Rounding to the nearest whole number, we find there are approximately 2398 seniors.
Therefore, the approximate number of students in each grade level is:
Freshmen: 35
Sophomores: 2698
Juniors: 3083
Seniors: 2398
Note: These values are approximations because we rounded the numbers.