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. What is the original number?
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Question 76046This question is from textbook Algebra 1 Expressions, Equations, and Applications
: 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. What is the original number?
This question is from textbook Algebra 1 Expressions, Equations, and Applications
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 digit
:
"A two-digit number is five times its units digit." says:
10x + y = 5y
10x = 5y - y
10x = 4y
x = 4/10y
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
:
y = x + 3; simplified, divided by 9
;
What is the original number?
:
Substitute .4y for x in y = x + 3, solve for y
y = .4y + 3
y - .4y + 3
.6y = 3
y = 3/.6
y = 5
:
x = .4y
x = .4(5)
x = 2
:
Original number is 25
:
(which is 5 times 5)
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