The difference between the two numbers is 14.The larger number is twice the smaller number increased by 1. Find the numbers

Question

Define the variables. Write a system of equations and solve the system.

Answer 1

Let a = the smaller number and b = the larger.

b - a = 14

b = 2a + 1

Now, there are a few ways to do this, but since one equation is already solved for one of the variables, let's use substitution. That means we can swap out what's on one side of the = for what's on the other since they are the same (equal).

2a + 1 - a = 14

a = 13

b = 2(13) + 1

b = 27