The ages of the three children in a family are as follows: The middle child is one year older than the youngest, while the oldest is three times as old as the youngest. If the sum of their ages is #21# years, what are their ages?

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Answer 1 · 2017-08-07T13:01:23

Their ages are #4,5 and 12#

It is possible to use one variable to define the ages of all #3# children, because we are told how their ages relate to each other.

Choose the age of the youngest child to be #x#.
It is easier to add and multiply than subtract and divide.

The youngest age is #color(blue)(x)# years old

The middle child is #1# year older. This means the age is #color(red)(x+1)#

The oldest child is #3# times older than the youngest, so, #color(green)(3x)#

The sum of their ages is #21# years. Add the ages together:

#color(blue)(x)+ color(red)(x+1) +color(green)(3x) =21#

#5x +1 = 21#

#5x = 21-1#

#5x =20#

#x=4#

#x+1 = 5 and 3x = 12#

Their ages are #4,5,12#

Check" #4+5+12 =21#