Answer:
47
Explanation:
You want a two-digit number such that three times the tens digit is 2 less than twice the units digit, and twice the number is 20 greater than the number obtained by reversing the digits.
Setup
Let x and y represent the tens digit and ones digit, respectively. The given relations can be written as equations as follows:
3x = 2y -2 . . . . 3 times tens digit is 2 less than 2 times ones digit
2(10x+y) = (10y +x) +20 . . . . 2 times the number is 20 more than reversed
Solution
Simplifying the equations and expressing them in standard form, we have ...
3x -2y = -2
20x +2y = x +10y +20 ⇒ 19x -8y = 20
Subtracting 4 times the first equation from the second, we have ...
(19x -8y) -4(3x -2y) = (20) -4(-2)
7x = 28 . . . . . . . simplify
x = 4
Substituting into the first equation, we have ...
3(4) -2y = -2
12 +2 = 2y . . . . . add 2y+2
7 = y . . . . . . . . divide by 2
The two-digit number is 47.