John's father is 5 times older than John and John is twice as old as his sister Alice. In two years, the sum of their ages will be 58. How old is John now?

1 Answer
Sep 25, 2017

John's present age is 8 years.

Explanation:

Let John's age be #x#.

Given that :
1. John's father is 5 times older than John

If #y# is the age of John's father, then
# y = 5x#

  1. John is twice as old as his sister Alice.
    So if #z # is age of Alice, then

#x = 2z# i.e. # z = x/2#

  1. In two years, the sum of their ages will be 58.

In two years.

John will be # x+ 2#
John's father will be # y + 2 = 5x +2# and
Alice will be #z + 2 = x/2 +2 #

Therefore
#(x+2) + (5x +2) + (x/2 +2) = 58#

# x+2 +5x +2 + 0.5x +2 = 58#

# x+5x + 0.5x +2 +2 +2 = 58#

# 6.5x +6 = 58#

# 6.5x = 58-6#

# x = 52/ 6.5#

# x = 520/ 65#

# x = 8# --------John's present age.

Fathers present age #y#= #5x = 40# years.
Alice present age #z# = #0.5x = 4# years.

Answer : John's present age is 8 years.