Question

A neighborhood recreation program serves a total $280$ children who are either $11$ years old or $12$ years old. The sum of the children's ages is $3,238$ years. How many $11$ year old children does the recreation program serve?

• A. $54$
• B. $122$
• C. $132$
• D. $158$
• E. $208$

Answer 1

The correct option is B $122$

Let the number of $11$ years children is $x$ and $12$ year children is $y$.

$\therefore 11x+12y=3238$.....(1)

$\Rightarrow x+y=280$

$\Rightarrow y=280-x$

Sustitute the value of $y$ in (1)

$\Rightarrow 11x+12(280-x)=3238$

$\Rightarrow 11x+3360-12x=3238$

$\Rightarrow 11x-12x=3238-3360$

$\Rightarrow x=122$

Hence, number of $11$ year children are $122$.