The difference between two numbers is 80. One of them is six times smaller than the other. find these numbers.

1. Let the first number be x, and the second number y. According to the condition, the difference between these numbers is 80. Let’s compose the first equation:

x – y = 80;

2. According to the condition, the second number is equal to y, 6 times less than the first, the number is equal to x. Let’s make the equation:

x = 6y;

3. Let’s compose a system of equations and solve it by the substitution method. To do this, we substitute the second equation into the first:

{x – y = 80;

{x = 6y;

6y – y = 80;

5y = 80;

y = 80/5;

y = 16;

Then, we find the second number by substituting the value of y:

x = 6 * 16 = 96;

Answer: x = 96, y = 6.