1963 TMTA High School Algebra I Contest Problem 8

Problem

$\frac{a^(-1) + b^(-1)}{(a+b)^(-1)}$ is equal to

$\text{(A)} \quad K-10 \quad \text{(B)} \quad 5K-20 \quad \text{(C)} \quad \frac{K-4}{5} \quad \text{(D)} \quad \frac{K}{5}-4 \quad \text{(E) NOTA}$

Note that there are $5$ dimes in one half dollar, so there are $(K-4)(5) = 5K-20$ dimes in $K-4$ half dollars. The answer is $\boxed{\text{(B)}}.$

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 7	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 9