# Seven years ago, Elise was half the age that she will be in six years. How old is Elise now?

## Question:

Seven years ago, Elise was half the age that she will be in six years.

How old is Elise now?

## Algebraic Equations:

Algebraic equations can be really helpful in in solving puzzles, because they help you model the situation in terms of known and an unknown. Once we represent the relation between the known and the unknown quantities, it remains simple arithmetic to get us to the solution.

The question mentions of Elise who, {eq}7 {/eq} year ago was half the age of that she will be in {eq}6 {/eq} years.

Let's consider that Elise's present age is {eq}X {/eq} years.

Now, {eq}7 {/eq} year ago, that means {eq}X-7 {/eq} years. Elise will be half the age that she will be in {eq}6 {/eq} years.

After {eq}6 {/eq} years mean, {eq}X+6 {/eq} and half of that means {eq}\displaystyle\frac{X+6}{2} {/eq}

So reframing what the question tells us...

{eq}\displaystyle{X-7}=\displaystyle\frac{X+6}{2} {/eq}

The only part left now is simple arithmetic operations.

{eq}2X-14=X+6\\ X=20 {/eq}

So, Elise is {eq}20 {/eq} years old at present. 