SOLUTION: A certain number of two digits is three times the sum of the digit. If 45 is added to it the digits are reversed.Find the number.
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Question 954402: A certain number of two digits is three times the sum of the digit. If 45 is added to it the digits are reversed.Find the number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let a = the 10's digit
let b = the units
then
10a + b = the number
:
A certain number of two digits is three times the sum of the digit.
10a + b = 3(a + b)
10a + b = 3a + 3b
10a - 3a = 3b - b
7a = 2b
If 45 is added to it the digits are reversed.Find the number.
10a + b + 45 = 10b + a
10a - a + 45 = 10b - b
9a + 45 = 9b
simplify, divide by 9
a + 5 = b
a = b - 5
Back to our 1st equation, replace a with (b-5)
7(b-5) = 2b
7b - 35 = 2b
7b - 2b = 35
5b = 35
b = 7
find a using the equation; a = b - 5
a = 7 - 5
a = 2
Our number: 27
:
:
Confirm this in the statement:
"If 45 is added to it the digits are reversed"
27 + 45 = 72
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