The larger of two numbers is one more than four times the smaller number. if the sum of the numbers is 106, find the numbers.

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