Need to find an equation to help solve word problem

Question

Here is the word problem:

today, billy has $10. Each day he earns $1. Nancy has $4, she makes $2 everyday. In how many days will they have the same amount of money?

Answer 1

Let x = # days Billy and Nancy have been earning money

Then an equation representing the amount of money Billy has earned:

B= 10 + 1x (Billy started with $10 and earns $1 each day)

N = 4 + 2x (Nancy started with $4 and earns $2 each day)

We want to know how many days it will take for both to have the same amount of money, so set the expressions representing the amounts earned equal to each other and solve for x (#of days of earning).

4 + 2x = 10 + 1x

x = 6

Check:

After 6 days Billy will have $10 + 6(1) = $16

After 6 days Nancy will have $4 + 6(2) = $16