# Word Problem issue

• January 29th 2010, 09:47 AM
jww123
Word Problem issue
If someone knows how to solve this problem could you explain to me in detail how you do it and how you figured out what to do?

Sarah is twice as old as John. Six years ago, Sarah was 4 times as old as John was then. How old is John now?

Thanks in advance for any help.
• January 29th 2010, 10:01 AM
e^(i*pi)
Quote:

Originally Posted by jww123
If someone knows how to solve this problem could you explain to me in detail how you do it and how you figured out what to do?

Sarah is twice as old as John. Six years ago, Sarah was 4 times as old as John was then. How old is John now?

Thanks in advance for any help.

Let S be Sarah's age and let J be John's age and base the age now as 0

$S = 2J$

$S-6 = 4(J-6) \: \: \rightarrow \: \: S = 4J-18$

Solve the simultaneous equations. I would recommend taking the first equation from the second to eliminate S.
• January 29th 2010, 10:19 AM
jww123
thank you this is the way that it shows that it's done, but I don't get it??

Sarah is twice as old as John
S=2J "this i get
Six years ago Sarah was 4 times as old as John was then.
S-6=4(J-6) "this I get"

Substituting 1 and 2 "I don't get any of this below"

2J-6=4(J-6)
2J-6=4J-24 <----- Were did they get the 24 from?
18=2J <----- Were did they get the 18 from?
9=J
• January 29th 2010, 10:26 AM
e^(i*pi)
Quote:

Originally Posted by jww123
thank you this is the way that it shows that it's done, but I don't get it??

Sarah is twice as old as John
S=2J "this i get
Six years ago Sarah was 4 times as old as John was then.
S-6=4(J-6) "this I get"

Substituting 1 and 2 "I don't get any of this below"

2J-6=4(J-6)
2J-6=4J-24 <----- Were did they get the 24 from?
18=2J <----- Were did they get the 18 from?
9=J

There is a rule which name I've forgotten that says $a(b+c) = ab + ac$ therefore $4(J-6) = 4J-24$. Then, in order to isolate S I added 6 to both sides

$S = 4J-18$

J does equal 9 so your maths is fine
• January 29th 2010, 10:42 AM
jww123
Thanks, I appreciate it.

a(b + c) = ab + ac is a Distributive property