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?

Question

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?

Answer 1

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 $\color{blue}{\bf 2}K - 4 = \color{blue}{\bf x} K - 4$?

Answer 2

Let $S$ be Sam's current age, and let $K$ be Kelly's current age. Then $K-2$ is Kelly's age two years ago, so the statement

Sam's age is twice the age Kelly was two years ago

means that $$S=2(K-2).$$ Applying the distributive property, this becomes $$S=2K-4.$$ Thus, in four years, Sam's age will be $S+4$, which is equal to $2K$.

Answer 3

First, your mistake is in understanding the auestion. that's written sam's age is twice of anita's before 2 years. It means that nowadays his age is twice then the age anita had before ywo years. Nobody had given you that before h2 years the ratio of ages was twice.

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Now, I'll suggest a way to solve it. let's assign sam's age today as $s$ and anita's age in $a$. we are given tht sam's age nowadays is twice the age of anita before two years. We can write it in equlation-form: $$s=2\dot(a-2)=2a-4$$. Now we are asked to calculate the radio between sam's age in 4 years (a.k.a $s+4$) and anita's age today ($a$), so the radio can be expressed after evaluation as $$\frac{s+4}{a}=\frac{2a-4+4}{y}=\frac {2y}{y}=2$$. that's I think the right answer also.

Answer 4

Others did already answer what you did wrong. I just want to show you how you can solve this kind of question.

Formalize question

$x := $"Age of Sam today"

$y := $"Age of Kelly today"

$t := $"Factor you're looking for"

$x, y \in \mathbb{N}, t \in \mathbb{R}_0^+$

I) $x = 2 \cdot (y-2)$

II) $x+4=t \cdot y$

Calculate answer

I) in II): $2 \cdot (y-2)+4 = t \cdot y$

$\Leftrightarrow 2 \cdot (y-2+2) = t \cdot y$

$\Leftrightarrow 2 \cdot y = t \cdot y$

$\Leftrightarrow t = 2$