Question

Find the two-digit number satisfying the following two conditions.

Answer 1

Let x = the 10's digit
Let y - units digit
then
10x + y = original number
:
Write and equation for each statement:
;
"the units digits of a two-digit number is 3 more than twice the tens digit."
y = 2x + 3
:
"If the digits are reversed, the new number is 9 less than 4 times the original number."
10y + x = 4(10x+y) - 9
10y + x = 40x + 4y - 9
10y - 4y = 40x - x - 9
6y = 39x - 9
:

Find the original number.
:
Substitute (2x+3) for y in the above equation:
6(2x+3) = 39x - 9
12x + 18 = 39x - 9
18 + 9 = 39x - 12x
27 = 27x
x = 1
:
Then using y = 2x+3
y = 2(1) + 3
y = 5
:
Original number = 15
:
:
Check solution in the statement:
"If the digits are reversed, the new number is 9 less than 4 times the original number."
51 = 4(15) - 9

Answer 2

The answer to the question is 72. This can be found either by trial and error, or by setting up a system of equations.