If Sam's age is twice the age Kelly was two years ago, Sam's age in four years will be how many times Kelly's age now? 1. If Sam's age is twice the age Kelly was two years ago, Sam's age in four years will be how many times Kelly's age now? (A) .5 (B) 1 (C) 1.5 (D) 2 (E) 4 So say at -2 years Sam's age is 12 and Kelly's age is 6. Add one to each year Sam passes. -2 = 12 -1 = 13 0 = 14 (this would be the present year) 1 = 15 2 = 16 3 = 17 4 = 1 In four years, Sam will be 18 years old. With the same process with Kelly: -2 = 6 -1 = 7 0 = 8 Kelly is now 8 years old. 18/8 is 2.25, which is not part of the answer choice, and the answer is apparently D) 2. What did I do wrong?

Let $S$ denote Sam's age now, and let $K$ denote Kelly's age now.

$(1)$: We are given that Sam's **current age** is twice the age Kelly was $2$ years **ago** , so we have that $$S = \text{twice}\left(\text{Kelly's age 2 years ago}\right)\tag{1}$$

$(2)$ We are also asked to determine what multiple $x$ of $K$ will be equal to Sam's age **4 years from now** : $$\text{When will}\;xK\;\text{equal}\; S+ 4\quad ?\tag{2}$$

So we need to determine which of the given values for $x$ makes the following system " **match** ":

$$S = 2(K - 2) \iff S = \color{blue}{\bf 2}K - 4\tag{1}$$

$$S + 4 = xK \iff \;\;S = \color{blue}{\bf x}K - 4\tag{2}$$

Now, what value must $\color{blue}{\bf x}$ be to make $\color{blue}{\bf 2}K - 4 = \color{blue}{\bf x} K - 4$?