SOLUTION: A two-digit number is five times its units digit. if the digits are reversed the resulting number is 27 more than the original number, find the original number?

Question 115477This question is from textbook algebra 1
: A two-digit number is five times its units digit. if the digits are reversed the resulting number is 27 more than the original number, find the original number? This question is from textbook algebra 1

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
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?

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