SOLUTION: Hi, I need help with a math problem: The ratio between the ages of John and David is 6:5. In 7 years time the ratio between their ages will be 7:6. How old are they today?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Hi, I need help with a math problem: The ratio between the ages of John and David is 6:5. In 7 years time the ratio between their ages will be 7:6. How old are they today?       Log On


   



Question 1005488: Hi,
I need help with a math problem:
The ratio between the ages of John and David is 6:5. In 7 years time the ratio between their ages will be 7:6. How old are they today?
Thanks for the help.
- E.S.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = John's age now
Let +d+ = David's age now
given:
(1) +j%2Fd+=+6%2F5+
(2) +%28+j%2B7%29+%2F+%28+d%2B7+%29+=+7%2F6+
-------------------------
Multiply both sides of (1) by +d+
(1) +j+=+%286%2F5%29%2Ad+
------------------
Multiply both sides of (2) by +6%2A%28+d%2B7+%29+
(2) +6%2A%28+j%2B7+%29+=+7%2A%28+d%2B7+%29+
(2) +6j+%2B+42+=+7d+%2B+49+
-----------------------
Substitute (1) into (2)
(2) +6%2A%28+%286%2F5%29%2Ad+%29+%2B+42+=+7d+%2B+49+
(2) +6%2A%28+%286%2F5%29%2Ad+%29+-+7d+=+7+
Multiply both sides by +5+
(2) +36d+-+35d+=+35+
(2) +d+=+35+
and
(1) +j+=+%286%2F5%29%2Ad+
(1) +j+=+%286%2F5%29%2A35+
(1) +j+=+42+
---------------
John is 42 and David is 35
---------------------
check:
+42%2F35+=+6%2F5+
+%28+6%2A7+%29+%2F+%28+5%2A7+%29+=+6%2F5+
OK
and
+%28+42+%2B+7+%29+%2F+%28+35+%2B+7+%29+=+7%2F6+
+49%2F42+=+7%2F6+
+%28+7%2A7+%29+%2F+%28+6%2A7+%29+=+7%2F6+
OK