There are 75 students in classes A and B altogether. There are 61 students in classes A and C altogether. The ratio of the number of students in Class B to Class C is 5:3. How many students are there in Class A?
+287 Let $a$ be the number of students in class A;
$b$ be the number of students in class B;
and $c$ be the number of students in class C.
The assumptions give you three equations in 3 unknowns $a$, $b$, and $c$.
\begin{eqnarray*}
a+b &=& 75 \\
a+c &=& 61 \\
b/c &=& 5/3
\end{eqnarray*}
The answer is $a$ after you solve this system of equations.
