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.

Question

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.

Answer 1

Here's what we know:

a + b = 106 (their sum equals 106)

b = 4a + 1 (the larger number is 1 more than 4 times the smaller)

 

We have a value for a variable, so we can plug it in:

a + 4a + 1 = 106

5a + 1 = 106

Subtract 1:

5a = 105

Divide by 5:

a = 21

 

Now that you know a, you can use that to find b by plugging that into either or both equations.

Answer 2

Let S = smaller and L = larger

L = 4S + 1

Sum = 4S +1 + S = 5S + 1 = 106

5S = 105....you solve it from here!