Question 115477
Let x = 10's digit and y = the units digit
:
Write an equation for what it says, simplify as much as you can:
"A two-digit number is five times its units digit."
10x + y = 5y
10x = 5y - y
10x = 4y
x = {{{(4y)/10}}}
x = .4y
:
"if the digits are reversed the resulting number is 27 more than the original number"
10y + x = 10x + y + 27
:
10y - y = 10x - x + 27
:
9y = 9x + 27
:
Simplify, divide by 9:
y - x + 3
:
Substitute .4y for x in the above equation, find y
y = .4y + 3
y - .4y = 3
.6y = 3
y = 3/.6
y = 5
:
x = .4y
x = .4(5)
x = 2
:
Our original two digit number is 25:
:
:
Check our solution in the statement:
 "if the digits are reversed the resulting number is 27 more than the original number, "
52 = 25 + 27; confirms our solution
:
Did this make sense to you? Not that hard, right?