one number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. find the two numbers.

Define the two numbers as

x

x+7

2 (x+7) + 1 = 5x

2x + 14 + 1 = 5x

15 = 3x

3x = 15

x = 5

x+7 = 12

One number is 7 less than another. 5 is 7 less than 12.

Twice the second number = 2*12 = 24

Is 24, 1 less than 5 times the first number.

5*5 = 25

25-24 = 1

The smaller of the two numbers is 5.