Ten years ago, a man was 3 times as old as his son. In 6 years, he will be twice as old as his son. How old is each now?

1 Answer
May 20, 2018

Answer:

The son is #26# and the man is #58#.

Explanation:

Consider their ages #10# years ago, now,and in #6# years time.

Let the son's age #10# years ago be #x# years.
Then the man's age was #3x#

It is useful to draw a table for this

#ul(color(white)(xxxxxxx)"past" color(white)(xxxxxxx)"present"color(white)(xxxxxxx)"future")#
SON:#color(white)(xxxxx)x color(white)(xxxxxxx)(x+10)color(white)(xxxxxx)(x+16)#

MAN:#color(white)(xxxx)3xcolor(white)(xxxxxxx)(3x+10)color(white)(xxxxx)(3x+16)#

In #6# years time, the man's age will be twice his son's age.
Write an equation to show this.

#2(x+16) = 3x+16#

#2x +32 = 3x+16#

#32-16 = 3x-2x#

#16 = x#

Ten years ago, the son was #16# years old.

Use this value for #x# to find the ages in the table.

#ul(color(white)(xxxxxxx)"past" color(white)(xxxxxxx)"present"color(white)(xxxxxxx)"future")#
SON:#color(white)(xxxxx)16 color(white)(xxxxxxx)(26)color(white)(xxxxxxxx)(32)#

MAN:#color(white)(xxx.x)48color(white)(xxxxxxx)(58)color(white)(xxxxx..xx)(64)#

We see that #2xx32 =64# so the ages are correct.

The son is #26# and the man is #58#.