Question 78590: Joe is 10 years older than James. In 8 years, twice Joe's age will equal three times James's age. How old is each now?
{James is yrs., Joe is yrs.}
Found 2 solutions by ankor@dixie-net.com, attaboy15:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Write a simple equation for each statement:
:
"Joe is 10 years older than James."
Jo = Ja + 10
:
"In 8 years, twice Joe's age will equal three times James's age."
2(Jo + 8) = 3(Ja + 8)
2Jo + 16 = 3Ja + 24
2Jo = 3Ja + 24 - 16
2Jo = 3Ja + 8
:
Substitute (Ja+10) for Jo in the above equation, find Ja:
2(Ja+10) = 3Ja + 8
2Ja + 20 = 3Ja + 8
20 - 8 = 3Ja - 2Ja
Ja = 12 yrs, his age now
:
Jo is 10 years older; Jo = 22 yrs now
:
:
Check solution in the statement:
"In 8 years, twice Joe's age will equal three times James's age."
2(22 + 8) = 3(12 + 8)
2(30) = 3(20)
:
Make sense to you? Any questions?
Answer by attaboy15(1)  (Show Source):
You can put this solution on YOUR website! Joe is 10 years older than James. In 8 years twice Joe’s age will equal 3 times James age.
What are their ages now?
First, let’s determine their ages 8 years from now. Once that is determined, then we can just subtract 8 years from the answer to get their ages now.
If Joe’s age is X then James age is X-10
Here is the first equation to use.
2 times X = 3 times ( X – 10 ) or
2X=3(X-10) this can become the following
2X=3X-30 add 30 to each side and get the following
2X+30=3X now subtract 2X from each side and get
30=3X-2X 3X – 2X = 1X or just X so…..
30=X
So Joe’s age in 8 years is 30, James would be 20 (10 years younger) but their ages now would be
Joe - 30-8=22
James – 20-8=12
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