Call the numbers x and y. According to the first sentence, x = 4y + 1. According to the second sentence, x + y = 106. You can combine these two equations to find the values of these variables:
x + y = 106
4y + 1 + y = 106
5y = 105
y = 21
We have y, so now we can solve for x using either original equation:
x + y = 106
x + 21 = 106
x = 85
