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

#2**+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

#1**+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**+10 **

Best AnswerThe 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