SOLUTION: a principal walks in and said I am 4 times the age of my grandson and my son is 11 years younger than my daughter and my daughter is 30 years older than my grandson .. all of our a

Question 151720: a principal walks in and said I am 4 times the age of my grandson and my son is 11 years younger than my daughter and my daughter is 30 years older than my grandson .. all of our ages equal 196..how old is the principal????
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
principal walks in and said I am 4 times the age of my grandson and my son is 11 years younger than my daughter and my daughter is 30 years older than my grandson .. all of our ages equal 196..how old is the principal????
:
Let p = present age of principal
Let g = present age of grandson
Let s = present age of son
Let d = present age of daughter
;
Write an equation for each statement
" principal walks in and said I am 4 times the age of my grandson"
p = 4g
:
"my son is 11 years younger than my daughter"
s = d - 11
:
"my daughter is 30 years older than my grandson"
d = g + 30
or
g = (d - 30)
;
" all of our ages equal 196"
p + g + s + d = 196
:
Try to get all variables in terms of d:
p = 4g; and g = (d-30)
therefore:
p = 4(d-30)
p = (4d - 120)
;
Substitute for p, s, g in the total age equation
(4d-120) + (d-11) + (d-30) + d = 196
7d - 161 = 196
7d = 196 + 161
7d = 357
d =
d = 51 yrs age of the daughter
:
..how old is the principal????
;
We determined that p = 4d - 120
p = 4(51) - 120
p = 204 - 120
p = 84 yrs is the age of the principal
:
:
Check solution in the total equation
84 + (51-11) + (51-30) + 51 = 196
84 + 40 + 21 + 51 = 196
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