Question

Kirk has 12 dollars less than Jim. If Jim spends half of his money, and Kirk spends none, then Kirk will have two dollars more than Jim. How much money did they both start with?

Answer 1

Kirk started with 16 dollars, and Jim started with 28

Explanation:

Let's call K the amount of money Kirk has

Let's call J the amount of money Jim has

From the question, we know two things:

First, Kirk has 12 dollars less than Jim. So we can say:

J - 12 = K

Second, if Jim spends half of his money (so, divide J by 2), Kirk will have two dollars more than Jim. So:

J/2 + 2 = K

Now, we have two equations that both contain K. Instead of using K in the first equation, we can replace it with J/2 + 2 (because we know that K = J/2 + 2)

J - 12 = J/2 + 2

Let's get all of the variables (the Js) to one side of the equation. We can restate this as:

J = J/2 + 14 (by adding 12 to both sides of the equation)

And then:

J-J/2 = 14 (subtracting J/2 from both sides of the equation)

Let's get rid of that fraction by multiplying both sides by 2:

2(J - J/2) = 2(14)

2J - J = 28

And simplify this to:

J = 28

Jim starts with 28 dollars. As for Kirk:

J - 12 = K

28 - 12 = K

16 = K

Kirk starts with 16 dollars