Question

4.4.6 check your understanding
there are eleven 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 the situation is
part b: this equation has because
there are an unlimited number of combinations of real numbers whose sum is eleven
there are no combinations of real numbers whose sum is eleven
the number of boys or girls must be a whole number

Explanation:

Step1: Determine the total - member equation

The total number of members is 11, with \(b\) boys and \(g\) girls. So the equation is \(b + g=11\).

Step2: Analyze the number of solutions

The number of boys and girls must be non - negative whole numbers (you can't have a fraction of a person). The possible pairs \((b,g)\) are \((0,11),(1,10),(2,9),\cdots,(11,0)\). So the number of solutions is limited.

Answer:

Part A: \(b + g = 11\)
Part B: a limited number of solutions; the number of boys or girls must be a whole number