SOLUTION: The four children in the Dempsey family have a combined age of 25 years. Jennifer�s oldest brother is six times as old as she is. Her next-to-oldest brother is 5 years older than

Question 240250: The four children in the Dempsey family have a combined age of 25 years. Jennifer�s oldest brother is six times as old as she is. Her next-to-oldest brother is 5 years older than she is, and the youngest of her brothers is twice Jennifer�s age. How old is each of the Dempsey children?
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The four children in the Dempsey family have a combined age of 25 years.
Jennifer�s oldest brother is six times as old as she is.
Her next-to-oldest brother is 5 years older than she is, and the youngest of her brothers is twice Jennifer�s age.
How old is each of the Dempsey children?
:
Let the 4 children's ages be, j, a, b, c
:
Write an equation for each statement:
:
" The four children in the Dempsey family have a combined age of 25 years."
j + a + b + c = 25
:
" Jennifer�s oldest brother is six times as old as she is."
a = 6j
:
" Her next-to-oldest brother is 5 years older than she is,"
b = j + 5
:
" and the youngest of her brothers is twice Jennifer�s age."
c = 2j
:
How old is each of the Dempsey children?
:
Note that each are in terms of j, so we just substitute
j + a + b + c = 25
j + 6j + (j+5) + 2j = 25
combine like terms
j + 6j + j + 2j + 5 = 25
10j = 25 - 5
10j = 20
j =
j = 2
:
Now you use the equations we have, to find the ages a, b, c.
Check by adding them up and seeing if they equal 25
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