SOLUTION: 1. The present ages of Lewis and Brown are in the ratio 1:2. Three years from now, the ages will be in the ratio 3:5. Find the present ages of Lewis and Brown. 2. The ages of

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Question 533974: 1. The present ages of Lewis and Brown are in the ratio 1:2. Three years from now, the ages will be in the ratio 3:5. Find the present ages of Lewis and Brown.

2. The ages of Ashley and Mary are in the ratio 4:7. The sum of their ages is 22. Find the ages of Ashley and Mary.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = Lewis's age now
Let b = Brown's age now
given:
(1) +a%2Fb+=+1%2F2+
(2) +%28+a+%2B+3+%29+%2F+%28+b+%2B+3+%29+=+3%2F5+
------------------------
(2) ++a+%2B+3+=+%283%2F5%29%2A%28+b+%2B+3+%29+
(2) +5a+%2B+15+=+3%2A%28+b+%2B+3+%29+
(2) +5a+%2B+15+=+3b+%2B+9+
(2) +3b+-+5a+=+6+
and
(1) +a%2Fb+=+1%2F2+
(1) +a+=+%281%2F2%29%2Ab+
(1) +2a+=+b+
Substitute this into (2)
(2) +3%2A%282a%29+-+5a+=+6+
(2) +6a+-+5a+=+6+
(2) +a=+6+
and, since
(1) +2a+=+b+
(1) +b+=+12+
Their ages now are 6 and 12
check:
+6%2F12+=+1%2F2+
+%286%2B3%29%2F%2812%2B3%29+=+9%2F15+
+9%2F15+=+3%2F5+
OK
#2
Let a = Ashley's age now
Let b = Mary's age now
given:
(1) +a%2Fb+=+4%2F7+
(2) +a+%2B+b+=+22+
-------------
(1) +a+=+%284%2F7%29%2Ab+
Substitute this into (2)
(2) +%284%2F7%29%2Ab+%2B+b+=+22+
(2) +%2811%2F7%29%2Ab+=+22+
(2) +b+=+%287%2F11%29%2A22+
{2) +b+=+14+
and, since
(2) +a+%2B+b+=+22+
(2) +a+%2B+14+=+22+
(2) +a+=+8+
Ashley is 8 and Mary is 14
check answer:
(1) +a%2Fb+=+4%2F7+
(1) +8%2F14+=+4%2F7+
Multiply both sides by 14
(1) +8+=+8+
OK