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

2 Answers
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 3x.

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

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

(3x-3) + (x-3) = 66

4x=72

x=18

Hence, Cerise's age is 18 and Roliver's is 3(18) = 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 ... r=3c
Three years ago ...................r-3=3c-3" ".. Equation(1)

The sum of their ages was..(r-3)+(3c-3)=?
sixty six ...................(r-3)+(3c-3)=66" "..Equation(2)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider Eqn(1)

Add 3 to both sides

color(green)(r=3c...Equation(1_a))

Consider Eqn(2) and write as:

color(green)(r+3c-6=66)

Add 6 to both sides

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

Using Eqn(1_a) substitute for r in Eqn(2_a)

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 Eqn(1_a)

color(green)(r=3color(red)(c)color(white)("ddd") ->color(white)("ddd") r=3xxcolor(red)(72/6) =36 )

color(white)("ddddddddddddd")color(green)(bar(ul(|color(white)(./.)r=36color(white)(./.)|)))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

check

Eqn(1)

r-3=3c-3color(white)("dddd") ->color(white)("dddd") 36-3=3(12)-3

Eqn(2)

(r-3)+(3c-3)=66color(white)("ddd")->color(white)("ddd") 36-3+3(12)-3 = 66