1. ## Age problem

In the year 1988 , Q's age is 3 times of P's age . R is 25 years younger than Q . In 1995 , S's age is a quarter of P's age . In 2004 , S is 21 years old . How old is R when S was born ?

In 1988 , Q=3P

R=Q-25

In 1995 ,

$\displaystyle S=\frac{1}{4}(P+7)$

In 2004 ,

S=21 --- S will be 21-9 = 12 in 1995 .

$\displaystyle 12=\frac{1}{4}(P+7) \rightarrow P=41$

P is 41-7=34 years old in 1988 .

Q=3(34)=102 years old . Hence , R=102-25 =77years old .

In 1988 , S was 5 years old .

SO when S was born , R=77-5=72 years old .

It is wrong .. Where is my mistake ? Thanks

2. Originally Posted by thereddevils
In 1988 , Q=3P
R=Q-25

In 1995 ,
$\displaystyle S=\frac{1}{4}(P+7)$

In 2004 ,
S=21 --- S will be 21-9 = 12 in 1995 .

$\displaystyle 12=\frac{1}{4}(P+7) \rightarrow P=41$

P is 41-7=34 years old in 1988.
You shouldn't have subtracted 7. When you assigned variables, P was P's age in 1988. P+7 is P's age in 1995. P = 41.

Q=3(34)=102 years old . Hence , R=102-25 =77years old .
Q = 3(41) = 123. (123 years old!?!?)
R = 123 - 25 = 98

In 1988 , S was 5 years old .
SO when S was born , R=77-5=72 years old .
R = 98 - 5 = 93 years old.

01

3. Originally Posted by yeongil
You shouldn't have subtracted 7. When you assigned variables, P was P's age in 1988. P+7 is P's age in 1995. P = 41.

Q = 3(41) = 123. (123 years old!?!?)
R = 123 - 25 = 98

R = 98 - 5 = 93 years old.

01

Huh , but the choices are

(a) 19
(b) 21
(c) 26
(d) 30

4. Originally Posted by thereddevils
In the year 1988 , Q's age is 3 times of P's age . R is 25 years younger than Q . Mr F says: It's not clear whether P's present age or P's age in 1988 is meant.

In 1995 , S's age is a quarter of P's age . Mr F says: Again, it's not clear whether P's present age or P's age in 1995 is meant.

[snip]
Assuming the latter interpretation in each case, post #2 gives the correct answer. Since this is not one of the choices, some other interpretation of P's age is probably being used by the book. To be honest, I don't see the point in working through each of those different possible interpretations.

5. Hello, thereddevils!

Is there a typo?
The numbers don't seem to be reasonable.

In 1988: $\displaystyle Q$'s age was 3 times of $\displaystyle P$'s age; $\displaystyle R$ was 25 years younger than $\displaystyle Q.$

In 1995: $\displaystyle S$'s age is a quarter of $\displaystyle P$'s age.

In 2004: $\displaystyle S$ is 21 years old.

How old was $\displaystyle R$ when $\displaystyle S$ was born ?
Let $\displaystyle x$ = $\displaystyle P$'s age in 1988.

In 1988, we have:

. . $\displaystyle \begin{array}{c|c|c|c|} & P & Q & R \\ \hline \hline 1988 & x & 3x & 3x-25 \\ \hline\end{array}$

In 1985 (7 years later), we have:

. . $\displaystyle \begin{array}{c|c|c|c|c|} & P & Q & R & S \\ \hline \hline 1995 & x+7 & 3x+7 & 3x-18 & \frac{1}{4}(x+7) \\ \hline \end{array}$

In 2004 (9 years later), we have:

. . $\displaystyle \begin{array}{c|c|c|c|c|} & P & Q & R & S \\ \hline \hline 2004 & x+16 & 3x+16 & 3x - 9 & \frac{1}{4}(x+7)+9 \\ \hline \end{array}$

At this time, $\displaystyle S$ is 21: .$\displaystyle \tfrac{1}{4}(x+7) + 9 \:=\:21$

. . $\displaystyle \tfrac{1}{4}(x+7) \:=\:12 \quad\Rightarrow\quad x + 7 \:=\:48 \quad\Rightarrow\quad x \:=\:41$

Therefore, in 1988, $\displaystyle P$ was 41 years old . . . and $\displaystyle {\color{blue}Q}$ was 123 ??

6. Originally Posted by Soroban
Hello, thereddevils!

Is there a typo?
The numbers don't seem to be reasonable.

Let $\displaystyle x$ = $\displaystyle P$'s age in 1988.

In 1988, we have:

$\displaystyle \begin{array}{c|c|c|c|} & P & Q & R \\ \hline \hline 1988 & x & 3x & 3x-25 \\ \hline\end{array}$

In 1985 (7 years later), we have:

$\displaystyle \begin{array}{c|c|c|c|c|} & P & Q & R & S \\ \hline \hline 1995 & x+7 & 3x+7 & 3x-18 & \frac{1}{4}(x+7) \\ \hline \end{array}$

In 2004 (9 years later), we have:

$\displaystyle \begin{array}{c|c|c|c|c|} & P & Q & R & S \\ \hline \hline 2004 & x+16 & 3x+16 & 3x - 9 & \frac{1}{4}(x+7)+9 \\ \hline \end{array}$

At this time, $\displaystyle S$ is 21: .$\displaystyle \tfrac{1}{4}(x+7) + 9 \:=\:21$

. . $\displaystyle \tfrac{1}{4}(x+7) \:=\:12 \quad\Rightarrow\quad x + 7 \:=\:48 \quad\Rightarrow\quad x \:=\:41$

Therefore, in 1988, $\displaystyle P$ was 41 years old . . . and $\displaystyle {\color{blue}Q}$ was 123 ??

Well , the question .. the numbers i mean don seem to be reasonable to me too . Anyways , thanks for the help . Now i know how to solve questionslike this .