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?

Question

Avery Alexander · Accepted Answer

Rose is 16
Johnny is 24

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#

Kennedy Adams · Answer

undefined Let's represent Johnny's age as J and Rose's age as R. From the information given, we have two equations:

1. R = (2/3)J
2. (J + 5) + (R + 5) = 50

Substitute R from the first equation into the second equation:

(J + 5) + ((2/3)J + 5) = 50

Solve for J:

(5/3)J + 10 = 50 - 5

(5/3)J + 10 = 45

(5/3)J = 35

J = (3/5) * 35

J = 21

Substitute J = 21 into the first equation to find R:

R = (2/3) * 21

R = 14

Johnny's present age is 21 years old, and Rose's present age is 14 years old.