Question

Find the two-digit number satisfying the following two conditions.
1) Four times the units digit is six less than twice the tens digit.
2) The number is nine less than three times the number obtained by reversing the digits.

Will be awarded 50 points!

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.