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The age of a man 3 years ago was 11 times the age of his son. The ratio of their ages after 15 years will be 2:1

Guest Jan 24, 2015

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 #2
avatar+80785 
+10

The age of a man 3 years ago was 11 times the age of his son. The ratio of their ages after 15 years will be 2:1

And I assume you want to find their current ages??

Let x and y be the son's and father's ages, now...so we have

11(x-3)  = y-3 →   11x - 33 = y - 3  →   11x - 30 = y    (1)

2(x + 15) = y + 15 →  2x + 30 = y + 15 →  2x + 15 = y

And setting the "y's" equal, we have

11x - 30 = 2x + 15  rearrange

9x = 45   solve for x

x = 5, and that's the son's age now

And using (1)

11(5) - 30 = y  = 25  and that's the father's age now

 

CPhill  Jan 24, 2015
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 #1
avatar+18827 
+10

The age of a man 3 years ago was 11 times the age of his son. The ratio of their ages after 15 years will be 2:1

$$\small{\text{ s = son and m = man }$\\\\$
\begin{array}{lrcllrcl}
(1) & (m-3) &=& 11*(s-3) & | \quad (m-3) &=& 11s-33\\
(2) & \frac{m+15}{s+15} &=& \frac{2}{1} & | \quad m+15 &=& 2s+30\\
\hline
(2)-(1):& 18 &=& -9s+63 & | :9\\
&2 &=& -s+7\\
& s&=&5 \\
\hline
(1): & m-3 &=& 55-33\\
& m &=& 3+22\\
& m &=& 25 \\
\hline
\end{array}$$

The age of the man is 25 and the age of his son is 5.

heureka  Jan 24, 2015
 #2
avatar+80785 
+10
Best Answer

The age of a man 3 years ago was 11 times the age of his son. The ratio of their ages after 15 years will be 2:1

And I assume you want to find their current ages??

Let x and y be the son's and father's ages, now...so we have

11(x-3)  = y-3 →   11x - 33 = y - 3  →   11x - 30 = y    (1)

2(x + 15) = y + 15 →  2x + 30 = y + 15 →  2x + 15 = y

And setting the "y's" equal, we have

11x - 30 = 2x + 15  rearrange

9x = 45   solve for x

x = 5, and that's the son's age now

And using (1)

11(5) - 30 = y  = 25  and that's the father's age now

 

CPhill  Jan 24, 2015

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