Question

the sum of reciprocals of two consecutive even number is 7/24 one number
is 6 find the other

Answer 1

Let smaller even integer = x
Then larger even integer = x + 2

"Reciprocal of" means "1 over"

1 1 7
--- + ----- = ----
x x+2 24

The LCD is 24x(x+2). Multiply through by that LCD

1 1 7
24x(x+2)·--- + 24x(x+2)·----- = 24x(x+2)·----
x x+2 24

Cancel what will cancel

1 1 7
24x(x+2)·--- + 24x(x+2)·----- = 24x(x+2)·----
x x+2 24


24(x+2) + 24x = x(x+2)·7

24x + 48 + 24x = (x²+2x)7

48x + 48 = 7x² + 14x

0 = 7x² - 34x - 48

0 = (7x + 8)(x - 6)

Set first factor = 0

7x + 8 = 0
7x = -8
x = -8/7

Set second factor = 0

x - 6 = 0
x = 6

Discard fraction answer. Solution: smaller = 6, larger = 6+2 or 8