SOLUTION: Jill is 10 years younger than Brian. In 5 years, Jill will be two-thirds of Brian's age. how old will Jill be seven years from now?

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Question 1026666: Jill is 10 years younger than Brian. In 5 years, Jill will be two-thirds of Brian's age. how old will Jill be seven years from now?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jill is 10 years younger than Brian.
j = b - 10
:
In 5 years, Jill will be two-thirds of Brian's age.
j + 5 = 2%2F3(b+5)
get rid of the fraction, multiply both sides by 3
3(j+5) = 2(b+5)
3j + 15 = 2b + 10
3j = 2b + 10 - 15
3j = 2b - 5
Replace j with (b-10) from the first statement
3(b-10) = 2b - 5
3b - 30 = 2b - 5
3b - 2b = -5 + 30
b = 25 yrs is Brian's age
then
j = 25 - 10
j = 15 yrs is Jill's age
:
how old will Jill be seven years from now?
I'll let you figure this out

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = Jill's age now
Let +b+ = Brian's age now
--------------------------
(1) +j+=+b+-+10+
(2) +j+%2B+5+=+%28+2%2F3+%29%2A%28+b+%2B+5+%29+
---------------------------
Multiply both sides of (2) by +3+
(2) +3%2A%28+j+%2B+5+%29+=+2%2A%28+b+%2B+5+%29+
(2) +3j+%2B+15+=+2b+%2B+10+
(2) +2b+-+3j+=+5+
and
(1) +b+-+j+=+10+
--------------------
Multiply both sides of (1) by +2+
and subtract (2) from (1)
(1) +2b+-+2j+=+20+
(2) +-2b+%2B+3j+=+-5+
--------------------
+j+=+15+
and
(1) +j+=+b+-+10+
(1) 15+=+b+-+10+
(1) +b+=+25+
---------------
+j+%2B+7+=+15+%2B+7+
+j+%2B+7+=+22+
--------------------
In 7 yrs, Jill will be 22
--------------------
check answer:
(2) +j+%2B+5+=+%28+2%2F3+%29%2A%28+b+%2B+5+%29+
(2) +15+%2B+5+=+%28+2%2F3+%29%2A%28+25+%2B+5+%29+
(2) +20+=+%282%2F3%29%2A30+
(2) +60+=+2%2A30+
(2) +60+=+60+
and
(1) +j+=+b+-+10+
(1) 15+=+25+-+10+
(1) +15+=+15+
OK