Question 729754
let a = the 10's digit of the original number
let b = the units
:
"A two digit number and the resulting number when the digits are reversed are in the ratio 2:9."
{{{((10a+b))/((10b+a))}}} = {{{2/9}}}
Cross multiply
9(10a+b) = 2(10b+a)
90a + 9b = 20b + 2a
90a - 2a = 20b - 9b
88a = 11b
Simplify divide by 11
8a = b
:
"If the sum of the digits is 9,
a + b = 9
replace b with 8a
a + 8a = 9
9a = 9
a = 1
then
b = 8
:
18 is the original number
:
:
:
Check this
{{{18/81}}} = {{{2/9}}}