1959 AHSME Problems/Problem 17

Problem 17

If $y=a+\frac{b}{x}$ , where $a$ and $b$ are constants, and if $y=1$ when $x=-1$ , and $y=5$ when $x=-5$ , then $a+b$ equals: $\textbf{(A)}\ -1 \qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11$

Solution

Plugging in the x and y values, we obtain the following system of equations: $\begin {cases} 1 = a - b \\ 5 = a - \frac{b}{5} \end {cases}$ We can then subtract the equations to obtain the equation $4 = 0.8b$ , which works out to $b = 5$ .

Plugging that in to the original system of equations: $\begin {cases} 1 = a - 5 \\ 5 = a - \frac{5}{5} \end {cases}$ It is easy to see that $a = 6$ , and that $a+b$ is $\boxed{\textbf{(E) } 11}$ .

1959 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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1959 AHSME Problems/Problem 17

Problem 17

Solution

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