Question 76046
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)