SOLUTION: Sarah is 1/7 as old as Donald. In 9 years, Sarah's age will be 6 years more than 1/6 of Donald's age. How old are Sarah and Donald now?

Question 774061: Sarah is 1/7 as old as Donald. In 9 years, Sarah's age will be 6 years more than 1/6 of Donald's age. How old are Sarah and Donald now?
Found 2 solutions by josgarithmetic, DrBeeee:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
s = Sarah's age
d = Donald's age

_______________now____________________9 years from now
Sarah__________(1/7)d_________________s+9
Donald_________d______________________d+9

In 9 years, , and .
Think first how that makes sense.
...
When understood, simplify the "(1/6)"-"+9" equation, substitute for s, and solve first for s, before solving for d.

s=-3+(1/6)(d+9)
6s=-18+d+9
6s=d-9
substitute...

6d=7d-63
6d-7d=-63
d=63___________Donald's age
Now find s,
s=d/7
s=63/7
s=9___________Sarah's age

Sarah is 9 and Donald is 63
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let s = Sarah's current age
Let d = Donald's current age
The at present we have
(1) s = d/7
And in 9 years we have
(2) s + 9 = 6 + (d+9)/6 or
(3) s +3 = d/6 + 9/6 or
(4) s + 3/2 = d/6
Now substitute s of (1) into (4) and get
(5) d/7 + 3/2 = d/6 or
(6) d/6 - d/7 = 3/2 or
(7) (7-6)d/42 = 3/2 or
(8) d = 42*(3/2) or
(9) d = 21*3 or
(10) d = 63
Using (1) we get
(11) s = 63/7 or
(12) s = 9
Let's check these values with (2).
Is (9 + 9 = 6 + (63+9)/6)?
Is (18 = 6 + 72/6)?
Is (18 = 6 + 12)?
Is (18 = 18)? Yes.
Answer: Currently Sarah is 9 and Donald is 63.
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