# Roliver is three times as old as Cerise. Three years ago, the sum of their ages was sixty-six. Find their present age?

Feb 25, 2018

Cerise is currently 18 and Roliver is 54.

#### Explanation:

Let Cerise's current age be $x$,
If Roliver is currently three times her age, his current age is thus $3 x$.

So 3 years ago, Cerise must have been $x - 3$ years old and Roliver must have been $3 x - 3$ years old.

Since we know that the sum of their ages 3 years ago was 66, we can form an equation:

$\left(3 x - 3\right) + \left(x - 3\right) = 66$

$4 x = 72$

$x = 18$

Hence, Cerise's age is $18$ and Roliver's is $3 \left(18\right) = 54$.

Feb 25, 2018

Cerise's current age is 12
Roliver's current age is 36

#### Explanation:

Let Roliver's current age be $r$
Let Cerise's current age be $c$

Breaking the question down into its component parts

Roliver is ............................ r=?
tree timeas as old as Cerise $\ldots r = 3 c$
Three years ago $\ldots \ldots \ldots \ldots \ldots \ldots . r - 3 = 3 c - 3 \text{ } . . E q u a t i o n \left(1\right)$

The sum of their ages was..(r-3)+(3c-3)=?
sixty six $\ldots \ldots \ldots \ldots \ldots \ldots . \left(r - 3\right) + \left(3 c - 3\right) = 66 \text{ } . . E q u a t i o n \left(2\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider $E q n \left(1\right)$

$\textcolor{g r e e n}{r = 3 c \ldots E q u a t i o n \left({1}_{a}\right)}$

Consider $E q n \left(2\right)$ and write as:

$\textcolor{g r e e n}{r + 3 c - 6 = 66}$

color(green)(r+3c=72...Equation(2_a)

Using $E q n \left({1}_{a}\right)$ substitute for $r$ in $E q n \left({2}_{a}\right)$

color(green)(color(red)(r)+3c=72color(white)("ddd") ->color(white)("ddd") color(red)(3c)+3c=72

color(green)(color(white)("dddddddddddd")->color(white)("ddd")6c=72

Divide both sides by 6

color(green)(color(white)("ddddddd")->color(white)("d")bar(ul(|color(white)(./.) c=72/6=12color(white)(./.)|))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute for $c$ in $E q n \left({1}_{a}\right)$

$\textcolor{g r e e n}{r = 3 \textcolor{red}{c} \textcolor{w h i t e}{\text{ddd") ->color(white)("ddd}} r = 3 \times \textcolor{red}{\frac{72}{6}} = 36}$

$\textcolor{w h i t e}{\text{ddddddddddddd}} \textcolor{g r e e n}{\overline{\underline{| \textcolor{w h i t e}{\frac{.}{.}} r = 36 \textcolor{w h i t e}{\frac{.}{.}} |}}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

check

$E q n \left(1\right)$

$r - 3 = 3 c - 3 \textcolor{w h i t e}{\text{dddd") ->color(white)("dddd}} 36 - 3 = 3 \left(12\right) - 3$

$E q n \left(2\right)$

$\left(r - 3\right) + \left(3 c - 3\right) = 66 \textcolor{w h i t e}{\text{ddd")->color(white)("ddd}} 36 - 3 + 3 \left(12\right) - 3 = 66$