Question 498620: Mrs. Brooks lacks 7 years from being 5 times as old as her son. Six years from now she will lack three years from being three times as old as her son is then. Find each of their ages.
I came up with 2 equations, but I'm not sure where to go from there!
y = 5x - 7 and y + 6 = 3x - 3
Help me please!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let b = Mrs. B's present age
Let s = son's present age
;
Write an equation for each statement
:
"Mrs. Brooks lacks 7 years from being 5 times as old as her son."
b = 5s - 7
:
"Six years from now she will lack three years from being three times as old as her son is then."
b + 6 = 3(s+6) - 3
b + 6 = 3s + 18 - 3
b + 6 = 3s + 15
b = 3s + 15 - 6
b = 3s + 9
:
Using the first equation we can replace b with (5s-7), so be have
5s - 7 = 3s + 9
5s - 3s = 9 + 7
2s = 16
s = 8 yrs is son's age
:
Find B's age
b = 3(8) + 9
b = 24 + 9
b = 33 yrs
:
:
see if that checks out in the 1st statement
"Mrs. Brooks lacks 7 years from being 5 times as old as her son."
33 = 5(8) - 7
:
:
Regarding your equations, I think the 1st equation is right, however in the 2nd,
you did not recognize that they are speaking about the son's age in 6yrs also
so it should have been y + 6 = 3(x+6) - 3
:
You are obviously on the right track and have an understanding of these kind of problems. C
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