SOLUTION: A two digit number and the resulting number when the digits are reversed are in the ratio 2:9.If the sum of the digits is 9,Find the original number.

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Question 729754: A two digit number and the resulting number when the digits are reversed are in the ratio 2:9.If the sum of the digits is 9,Find the original number.
Found 2 solutions by ankor@dixie-net.com, lwsshak3:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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."
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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
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Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
A two digit number and the resulting number when the digits are reversed are in the ratio 2:9.If the sum of the digits is 9,Find the original number.
***
let u=units digit
let t=tens digit
t+u=9
t=9-u
original number=10t+u
reversed number=10u+t
(10t+u)/(10u+t)=2/9
(10(9-u)+u)/(10u+9-u)=2/9
(90-10u+u)/(10u+9-u)=2/9
(90-9u)/(9u+9)=2/9
810-81u=18u+18
99u=792
u=8
t=9-u=1
10t+u=10+8=18
original number=18