Question

4.4.6 check your understanding
there are twelve members of a schools club.
membership is open to all students enrolled in algebra 1 or higher math courses where b represents the number of boys and g represents the number of girls.
part a: an equation that represents this scenario is 12 = b + g
part b: this equation has infinitely many solutions because
there are an unlimited number of combinations of real numbers whose sum is twelve.
there are no combinations of real numbers whose sum is twelve.
the number of boys or girls must be a natural number.

Explanation:

Step1: Analyze Part A

The total number of club - members is 12, with boys as $b$ and girls as $g$. So the equation is $12 = b + g$.

Step2: Analyze Part B

The equation $12 = b + g$ has infinitely many solutions because for any real - number value of $b$, we can find a corresponding real - number value of $g$ such that $g=12 - b$. There are an unlimited number of combinations of real numbers whose sum is twelve.

Answer:

Part A: $12 = b + g$
Part B: infinitely many solutions because there are an unlimited number of combinations of real numbers whose sum is twelve.