Problems based on Numbers Test 6

Concept:Let the unknown number of members be a variable, form a quadratic equation from the total contribution, and reject the negative root because members cannot be negative.Explanation:Let the number of members be $x$.Contribution per member is $10$ more than $3$ times $x$, so it is $3x+10$.Total contribution is members multiplied by contribution per member.$$x(3x+10)=3000$$Expand:$$3x^2+10x-3000=0$$Use the quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ with $a=3$, $b=10$, $c=-3000$.$$x=\frac{-10\pm\sqrt{10^2-4(3)(-3000)}}{2(3)}$$$$x=\frac{-10\pm\sqrt{100+36000}}{6}$$$$x=\frac{-10\pm\sqrt{36100}}{6}$$$$x=\frac{-10\pm190}{6}$$The possible values are $x=\frac{-200}{6}$ and $x=\frac{180}{6}=30$.Since the number of members cannot be negative, $x=30$.Answer:The number of members is $30$, so the correct option is B.