SOLUTION: James is 19 times as old as Bill. Frank is 30 Years younger than James. In 6 Years James' age will be twice the sum of bill and Frank's ages then. How old is James? I'm getting

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: James is 19 times as old as Bill. Frank is 30 Years younger than James. In 6 Years James' age will be twice the sum of bill and Frank's ages then. How old is James? I'm getting       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 565512: James is 19 times as old as Bill. Frank is 30 Years younger than James. In 6 Years James' age will be twice the sum of bill and Frank's ages then. How old is James?
I'm getting a funny answer and would like to consult
Found 3 solutions by Leaf W., scott8148, josmiceli:
Answer by Leaf W.(135) About Me  (Show Source):
You can put this solution on YOUR website!
Bill: x
James: 19x
Frank: 19x - 30
Bill's age in six years: x + 6
James's age in six years: 19x + 6
Frank's age in six years: 19x - 24
Since James's age in six years will be twice the sum of Bill's and Frank's ages then, your equation is 19x + 6 = 2(x + 6 + 19x - 24)
Add like terms: 19x + 6 = 2(20x - 18)
Distribute the 2: 19x + 6 = 40x - 36
Add 36 to both sides: 19x + 42 = 40x
Subtract 19x from both sides: 42 = 21x
Divide both sides by 21: 2 = x
Therefore, Bill's is two years old. Plug this value into the expression for James's age, 19x.
19x = 19(2) = 38
***THEREFORE, JAMES IS 38 YEARS OLD.***
Hope I helped! =)

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"James is 19 times as old as Bill" ___ J = 19B ___ J / 19 = B

"Frank is 30 Years younger than James" ___ F = J - 30

"In 6 Years James' age will be twice the sum of bill and Frank's ages then" ___ J + 6 = 2(F + 6 + B + 6)

substituting ___ J + 6 = 2[(J - 30) + 6 + (J / 19) + 6]

J + 6 = 2J - 60 + 12 + (2J / 19) + 12 ___ 42 = J + (2J / 19) ___ 42 = 21J / 19 ___ 38 = J

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = James age now
Let +b+ = Bill's age now
Let +f+ = Frank's age now
given:
(1) +j+=+19b+
(2) +f+=+j+-+30+
(3) +j+%2B+6+=+2%2A%28+b+%2B+6+%2B+f+%2B+6+%29+
--------------------------
This is 3 equations and 3 unknowns, so
it should be solvable
(3) +j+%2B+6+=+2%2A%28+b+%2B+6+%2B+f+%2B+6+%29+
(3) +j+%2B+6+=+2b+%2B+2f+%2B+24++
(3) +j+-+2b+-+2f+=+24+-+6+
(3) +j+-+2b+-+2f+=+18+
--------------------
(1) +b+=+j%2F19+
Substitute (1) and (2) into (3)
(3) +j+-+2b+-+2f+=+18+
(3) +j+-+2%2A%28+j%2F19+%29+-+2%2A%28+j-30+%29+=+18+
(3) +j+-+2%2A%28+j%2F19+%29+-+2j+%2B+60+=+18+
Multiply both sides by +19+
(3) +19j+-+2j+-+38j+=+-798+
(3) +-21j+=+-798+
(3) +j+=+38+
and
(1) +b+=+j%2F19+
(1) +b+=+38%2F19+
(1) +b+=+2+
and
(2) +f+=+j+-+30+
(2) +f+=+38+-+30+
(2) +f+=+8+
James is 38, Bill is 2, and Frank is 8
check:
(3) +j+%2B+6+=+2%2A%28+b+%2B+6+%2B+f+%2B+6+%29+
(3) +38+%2B+6+=+2%2A%28+2+%2B+6+%2B+8+%2B+6+%29+
(3) +44+=+2%2A22+
(3) +44+=+44+
OK