SOLUTION: four times the sum of the digits of a two-digit number is equal to the number.if digits are reserved, the resulting number is 27 greater than the original number. what is the numbe

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Question 637661: four times the sum of the digits of a two-digit number is equal to the number.if digits are reserved, the resulting number is 27 greater than the original number. what is the number?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the 10's digit
let b = the units
then
10a+b = the original number
:
Write an equation for each statement:
:
"four times the sum of the digits of a two-digit number is equal to the number."
4(a+b) = 10a + b
4a + 4b = 10a + b
4b - b = 10a - 4a
3b = 6a
divide both sides by 3
b = 2a
:
"if digits are reserved, the resulting number is 27 greater than the original number."
10b + a = 10a + b + 27
10b - b = 10a - a + 27
9b = 9a + 27
divide by 9
b = a + 3
replace b with 2a (from the 1st statement)
2a = a + 3
2a - a = 3
a = 3
you can find b, I'm sure
what is the number?