Question

The sum of the digits of a two-digit number is 13.The tens digit is seventeen less than the square of the units digit. Find the number. ​

Answer 1

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Solution

Let x = units digit

x – 3 = tens digit

Equation

x + (x – 3) = 11

2x – 3 = 11

2x = 14

Answer

x = 7 (units digit)

x – 3 = 4 (tens digit)

Using the values above for units and tens, we find the number 47.

The tens digit of a number is twice the units digit. If the digits are reversed, the new number is 27 less than the original. Find the original number.

Solution

Let x = units digit

2x = tens digits

Then the original number is 10(2x) + x, the reserved number is 10(x) + 2x, and the new number is the original number less than 27.

Equation

10(x) + 2x = 10(2x) + x – 27

12x = 21x – 27

-9x = -27

x = 3 (units digit)

2x = 6 (tens digit)

Answer

The number is (6 X 10) + 3 or 63.