In a two-digit number the tens’ digit is 3 more than the units’ digit. The number itself is 17 times the units’ digit. Find the number.
To find the two-digit number, let's represent the units' digit as "x" and the tens' digit as "x + 3" since the tens' digit is 3 more than the units' digit.
The number itself can be expressed as (10 * tens' digit) + units' digit. In this case, it is 17 times the units' digit, so we can write:
(10 * (x + 3)) + x = 17x
First, let's simplify the left side of the equation:
10x + 30 + x = 17x
11x + 30 = 17x
Now, let's isolate the variable:
11x - 11x + 30 = 17x - 11x
30 = 6x
To solve for x, divide both sides of the equation by 6:
30/6 = x
5 = x
So the units' digit is 5.
Now, substitute the value of x (units' digit) back into the expression for the tens' digit:
Tens' digit = x + 3
= 5 + 3
= 8
Therefore, the two-digit number is 85.