Find 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 revers- ing the digits.

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.

Find 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 revers- ing the digits.​

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Setup

Solution

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Find 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 revers- ing the digits.