Question

[I lay my love on you]

Class A and Class B have the same number of students.

-The number of students in class A who took part in a mathematics competition is \(\frac{1}{3}\) of the studentsin Class B who did not take part.

-the number of students in class B who took part in a mathematics competition is \(\frac{1}{5}\)of the students in class A who đi not take part.

Find the ratio of the number of students in class A who did not take part in this competition to the number of students in class B who did not take part.

Answer 1

[Nguyễn Tất Đạt]

I call the number of students didn't take part in Mathemas Competition in class A & B are a & b respectively

(with condition: a & b \(\in\)N*)

,From the theme, we have: \(\frac{1}{3}b+a=\frac{1}{5}a+b\)(Because rhe number of students in 2 class is the same)

\(\Leftrightarrow\frac{b}{3}-b+a-\frac{a}{5}=0\Leftrightarrow\left(-\frac{2b}{3}\right)+\frac{4a}{5}=0\)

\(\Leftrightarrow\frac{4a}{5}-\frac{2b}{3}=0\Leftrightarrow\frac{12a-10b}{15}=0\Leftrightarrow12a=10b\)

\(\Rightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\) 

So the ratio of the number of student didn't take part of Class A & B is \(\frac{5}{6}.\)