# Mario is 15 years older than Pete. Two years from now, Mario will be four times as old as Pete. How old is each now?

Apr 27, 2018

Mario is $18$ years old and Pete is $3$ years old.

#### Explanation:

Let Pete be $x$ years old and Mario be $x + 15$ years old. After $2$ years, Pete will be $x + 2$ and Mario will be

$\left(x + 15 + 2\right) = x + 17$

Given Mario will be $4$ times as old as Pete

$x + 17 = 4 \left(x + 2\right)$

$x + 17 = 4 x + 8$

$- 3 x = 8 - 17$

$3 x = 9$

$x = 3$

Therefore, Pete's present age is $3$ yrs and Mario's present age is $x + 15$, i.e. $18$ yrs.

Apr 27, 2018

Pete is $3$, Mario is $18$

#### Explanation:

$M = 15 + P$ $\Leftarrow$ this is always true! Mario is always $15$ years older than Pete

and

$M = 4 P$ $\textcolor{w h i t e}{. .}$ (two years from now)

set them equal to eachother and solve

$15 + P = 4 P$

$15 = 3 P$

$5 = P$

Pete would be $5$ years old in $2$ years, and Mario would be $20$ years old. If our math is right, then Pete should be one quarter of Mario's age. Is that true?

$\frac{20}{4} = 5$, which is how old Pete is (in two years)! How old are he and Mario now?

Mario is $20 - 2$ or $18$ years old and Pete is $5 - 2$ or $3$.