SOLUTION: Mrs. Chen was 20 when her eldest child was born. Two years later, another child was born and four years after that, her youngest child was born. Now the averages of their four ages

Question 1111879: Mrs. Chen was 20 when her eldest child was born. Two years later, another child was born and four years after that, her youngest child was born. Now the averages of their four ages are 39. How old are Mrs. Chen and her three children now?
It would be great if an equation was written out first, thanks.
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Let x = the age of the youngest child. Then the next (= the middle) is (x+4); the oldest is ((x+4)+2) years old, and Mrs. Chen is (((x+4)+2)+20 years old, according to the condition. Since the average of four is 39 now, the sum of the ages of the four is 39*4 = 156. It gives you an equation x + (x+4) + ((x+4)+2) + (((x+4)+2)+20) = 156 4x + 36 = 156 4x = 156 - 36 = 120 ====> x = = 30. Answer. The members of the family are 30, 34, 36 and 56 years old. Check. = 39. ! Correct !

Solved.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = Mrs. Chen's age now.
Let = age of eldest child now
Let = age of middle child now
Let = age of youngest child now
--------------------------------------
(1)
( the difference in their ages will always be 20 yrs )
(2)
(3)
(4)
---------------------------------
(1)
(2)
(3)
By substitution:
(4)
(4)
(4)
(4)
(4)
and
(1)
(1)
(1)
and
(2)
(2)
(2)
and
(3)
(3)
(3)
--------------------------
Their ages are:
56, 36, 34, and 30
---------------------------
check:

OK

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