The first digit of a two-digit number is 4 greater than 20 and the product

The first digit of a two-digit number is 4 greater than 20 and the product is 21. Find this two-digit by two-digit number using the system of equations.

Let’s denote the first digit of this two-digit number by x.

In the initial data for this task, it is reported that the first digit of this two-digit number is more than the second digit by 4, therefore, the second digit of this number must be equal to x – 4.

Also in the problem statement it is said that if you multiply these 2 digits, the result will be 21, therefore, we can make the following equation:

x * (x – 4) = 21,

solving which, we get:

x ^ 2 – 4x = 21;

x ^ 2 – 4x – 21 = 0;

x = 2 ± √ (4 + 21) = 2 ± √25 = 2 ± 5;

x1 = 2 – 5 = -3;

x2 = 2 + 5 = 7.

Since the digit of a two-digit number cannot be negative, the value x = -3 is not suitable.

We find the second number:

x – 4 = 7 – 4 = 3.

Therefore, the required number is 73.

Answer: 73.