Question

Xavier and Madeleine's ages add up to 28. Xavier is 4 years older than half of Madeleine's age. How old will Xavier be in 2 years? A. 12 B. 14 C. 16 D. 18

Answer 1

In two years, Xavier will be 14 years old

Here, we want to get Xavier's age in 2 years

Let Xavier's current age be x and Madeleine's current age be m

The addition of the two will be 28

$x\text{ + m = 28}$

Secondly, we have that the age of Xavier x is 4 years older than half of Madeleine's age;

$x\text{ -4 = }\frac{m}{2}$

From the first equation, we can have a substition;

$m\text{ = 28 - x}$

Now, put this in the second equation;

$\begin{gathered} x-4\text{ = }\frac{28-x}{2} \\ 2(x-4)\text{ = 28-x} \\ 2x\text{ - 8 = 28 - x} \\ 2x+\text{ x = 28 + 8} \\ 3x\text{ = 36} \\ x\text{ = }\frac{36}{3} \\ x\text{ = 12} \end{gathered}$

Xavier's current age is 12

In the next two years, his age will be;

$12\text{ + 2 = 14}$