In a two-digit number, the units digit is times times the tens digit. Determine the original number, given that the product of the
two digits is of its value.
Denote the tens digit of the number by and the units digit by . If the units digit is 4 times the tens digit, then
If the product of the digits is of the number's value, then
This pair of equations can be solved by substitution. Substituting the expression for into the second order equation gives
This equation can be solved by factorisation.
But as is a two-digit number, its first digit cannot be 0. Therefore, .
Now substitute this value of into the first order equation to find .
The two-digit number is therefore 28.