the mean marks for a french test in a class of 30 boys and 20 girls are 60 and 70 respectively. find the mean mark for the whole class.

Step-by-step explanation:

Let, the number of boys be x and number of girls be y.

\begin{gathered}\\Mean \: marks \: of \: boys \\ = \frac{Total \: marks \: of \: boys }{Total \: number \: of \: boys} \\ \\ 70 = \frac{Total \: marks \: of \: boys}{ x } \\ \\ Total \: marks \: of \: boys = 70x \: \: (1) \\ Mean \: marks \: of \: boys \\ = \frac{Total \: marks \: of \: girls }{Total \: number \: of \: girls} \\ \\ 73 = \frac{Total \: marks \: of \: girls}{y} \\ \\ Total \: marks \: of \: girls = 73y \: \: (2) \\ Mean \: marks \: of \: entire \: students \\ = \frac{Total \: marks \: of \:students}{Total \: number \: of \: students } \\ \\ Mean \: marks \: of \: entire \: students \\ = \frac{Marks \: of \:boys + Marks \: of \: girls}{ Number \: of \: boys + Number \: of \: girls } \\ \\ from \: eq \: (1) \: and \: (2) \\ \\ 71 = \frac{70x + 73y}{x + y} \\ \\ 71(x + y) = 70x + 73y \\ \\ 71x + 71y = 70x + 73y \\ \\ 71x - 70x = 73y - 71y \\ \\ x = 2y \\ \\ \frac{x}{y} = \frac{2}{1} \\ \\ \frac{Number \: of \: boys}{Number \: of \: girls} = \frac{2}{1} \\ \\\end{gathered}

Meanmarksofboys

=

Totalnumberofboys

Totalmarksofboys

70=

x

Totalmarksofboys

Totalmarksofboys=70x(1)

Meanmarksofboys

=

Totalnumberofgirls

Totalmarksofgirls

73=

y

Totalmarksofgirls

Totalmarksofgirls=73y(2)

=

Totalnumberofstudents

Totalmarksofstudents

=

Numberofboys+Numberofgirls

Marksofboys+Marksofgirls

fromeq(1)and(2)

71=

x+y

70x+73y

71(x+y)=70x+73y

71x+71y=70x+73y

71x−70x=73y−71y

x=2y

y

x

=

1

2

Numberofgirls

Numberofboys

=

1

2

b

step-by-step explanation:

answerthe vertex form

step-by-step explanation: