Find two consecutive even integers such that the sum of their reciprocals is 9/40.
a. 8 and 9
b. 6 and 8
c. 8 and 10
d. 10 and 12

Question

Find two consecutive even integers such that the sum of their reciprocals is 9/40.
a. 8 and 9
b. 6 and 8
c. 8 and 10
d. 10 and 12

whpalmer4 · Answer

Let your first even integer be $n$.  Then $n+2$ is the second number.

You want the sum of their reciprocals to equal $\frac{9}{40}$

$$\frac{1}{n}+\frac{1}{n+2} = \frac{9}{40}$$Solve for $n$ and you've got the first number.  You'll get two solutions, but only one of them is an even integer...

whpalmer4 · Answer

As this is that bane of good instruction, the multiple-choice question, you could also just try plugging each answer choice into the formula and see which one works.  Better if you aren't under some incredible time pressure to actually go through the steps of solving it, in my opinion.

anonymous · Answer

Thank you so much!