Question

The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers. Find the two integers.

Answer 1

even integers :

...,2, 4, 6, 8, ...

Answer 2

two consecutive even integers differ by 2

Answer 3

for example :
4-2 = 2
8-6 = 2

Answer 4

if you let one even integer be q,
next even integer would be q+2

Answer 5

take the reciprocal of each of them and add as asked in the question

Answer 6

i dont understand this

Answer 7

actually its not as hard as im trying to make it

Answer 8

whats the reciprocal of q ?

Answer 9

1/q

Answer 10

good, whats the reciprocal of (q+2) ?

Answer 11

1/(q+2)

Answer 12

adding them you get :
\[\large \dfrac{1}{q} + \dfrac{1}{q+2}\]

Answer 13

set that equal to 7/24

Answer 14

\[\large \dfrac{1}{q} + \dfrac{1}{q+2} = \dfrac{7}{24}\]

Answer 15

does that make sense so far

Answer 16

i dont see ho 1+1 will =7 but ok

Answer 17

how*

Answer 18

1+1 is never 7
it equals 2 sometimes though

Answer 19

you're **given** that the sum equals 7/24

Answer 20

oh ok lol im kinda following

Answer 21

good, look at the options

Answer 22

based on that equation, you can eliminate few options ?

Answer 23

it has to be c or d because those are the only options with that set up

Answer 24

Exactly!

Answer 25

now how do i know which one it is i have no idea

Answer 26

maybe lets try option C :
plugin q = 6 into the equation and see if it satisfies