SOLUTION: nine times a two digit number is the same as twice the number obtained on interchanging the digits of the number.If one digit of the number exceeds the other by 7,find the number.
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Question 628279: nine times a two digit number is the same as twice the number obtained on interchanging the digits of the number.If one digit of the number exceeds the other by 7,find the number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let x = the 10's digit
let y = the units
then
10x+y = "the number"
and
10y+x = "the number reversed
:
write an equation for each statement
:
"nine times a two digit number is the same as twice the number obtained on
interchanging the digits of the number."
9(10x+y) = 2(10y+x)
90x + 9y = 20y + 2x
90x - 2x = 20y - 9y
88x = 11y
simplify, divide by 11
8x = y
;
"If one digit of the number exceeds the other by 7,"
y = x + 7 (y has to be the larger number)
replace y with 8x
8x = x + 7
8x - x = 7
7x = 7
x = 1
then
y = 8
:
18 is the original number
:
:
Check this in the 1st statement
9(18) = 2(81)
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