1. **State the problem:** A school has admitted 480 senior one students divided into four classes A, B, C, and D.
Class A has 80 students.
The ratio of students in class B to class C is 2:3.
The number of students in class A is twice the number in class D.
We need to find the number of students in class C to determine how many single seater chairs are needed.
2. **Define variables:** Let the number of students in class D be $d$.
Then, the number of students in class A is $80$ (given), and $80 = 2d$.
3. **Find $d$:**
$$80 = 2d \implies d = \frac{80}{2} = 40$$
4. **Express students in classes B and C:**
Let the number of students in class B be $b$ and in class C be $c$.
Given the ratio $b:c = 2:3$, so $b = 2k$ and $c = 3k$ for some $k$.
5. **Use total students to find $k$:**
Total students = $480$.
Sum of students in all classes:
$$80 + b + c + d = 480$$
Substitute $b = 2k$, $c = 3k$, and $d = 40$:
$$80 + 2k + 3k + 40 = 480$$
$$120 + 5k = 480$$
$$5k = 480 - 120 = 360$$
$$k = \frac{360}{5} = 72$$
6. **Find number of students in class C:**
$$c = 3k = 3 \times 72 = 216$$
**Final answer:** The number of students in class C is $216$, so the academic officer needs to get 216 single seater chairs for class C.
Class Students
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