Jill is twice as old as her brother and half as old as her father. In 22 years, her brother will be half as old as his father. How old is Jill now?

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Answer 1 · 2018-05-29T22:02:53

Jill is #22# years old.

Let Jill's age be #j#. Let Jill's brothers age be #b#. Let Jill's father's age by #f#.

"Jill is twice as old as her brother"

#j = 2b#

"Jill is half as old as her father"

#j = 1/2 f#

"In 22 years, her brother will be half as old as his father"

#b+22=1/2(f+22)#

We have three equations and three unknowns, so we can solve the system:

[1] #j = 2b#
[2] #j = 1/2f #
[3] #b +22= 1/2(f + 22)#

There are many ways to achieve the result. I will show one way.
Let's substitute [1] into [2]:

#2b = 1/2f#

[4] #b = 1/4 f#

Now let's substitute [4] into [3]:

#1/4f +22 = 1/2(f+22)#

#1/4f + 22 = 1/2f+11#

#1/4f = 11#

[5] #=>f = 44#

Now let's use [5] in [2]:

#j = 1/2(44)#

[6] #=> j = 22#

We could stop here, since we have found Jill's age, but let's just solve the entire system for completion's sake.

Lastly, let's use [6] in [1]:

#22 =2b#

[7] #=>b = 11#

Our result is the combination of [5], [6], and [7]:

#=> f = 44#
#=> j = 22#
#=> b = 11#

Hence,

Jill is #22# years old. Jill's brother is #11# years old. Jill's father is #44# years old.