Rose is two thirds as old as Johnny, in 5yrs the sum of their ages will be 50yrs, how do you find their present ages?

1 Answer
Sep 4, 2015

Answer:

Rose is 16
Johnny is 24

Explanation:

Define
#color(white)("XXX")r#: Rose's age
#color(white)("XXX")j#: Johnny's age

We are told
#color(white)("XXX")r=2/3j#

#color(white)("XXX")rarrcolor(white)("XXX")"[1]"color(white)("XXX")3r-2j=0#

and
#color(white)("XXX")(r+5)+(j+5) = 50#

#color(white)("XXX")rarrcolor(white)("XXX")"[2]"color(white)("XXX")r+j = 40#

Multiplying [2] by 2
#color(white)("XXXXXXXX")[3]color(white)("XXX")2r + 2j = 80#

Adding [1] and [3]
#color(white)("XXXXXXXX")[4]color(white)("XXX")5r = 80#

Dividing [4] by #5#
#color(white)("XXXXXXXX")[5]color(white)("XXX")r=16#

Substituting #16# for #r# in [1] (and simplifying
#color(white)("XXXXXXXX")[6]color(white)("XXX")j=24#