SOLUTION: Rick and sandy bought some raffle tickets together and won the prize of $3,600. if rick and sandy agreed to split the winnings at a ratio of 8 to 7 (ricks winnings to sandys winnin

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Question 585812: Rick and sandy bought some raffle tickets together and won the prize of $3,600. if rick and sandy agreed to split the winnings at a ratio of 8 to 7 (ricks winnings to sandys winnings) how much did each of them receive?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let r = Rick's share
Let s = Sandy's share
given:
(1) +r+%2B+s+=+3600+
(2) +r%2Fs+=+8%2F7+
-------------
Multiply both sides of (2) by +7s+
(2) +7r+=+8s+
(2) +r+=+%288%2F7%29%2As+
Substitute this into (1)
(1) +%288%2F7%29%2As+%2B+%287%2F7%29%2As+=+3600+
(1) +%2815%2F7%29%2As+=+3600+
(1) +s+=+%287%2F15%29%2A3600+
(1) +s+=+1680+
and, since
(1) +r+%2B+s+=+3600+
(1) +r+%2B+1680+=+3600+
(1) +r+=+1920+
Rick gets $1,920
Sandy gets $1,680
check:
(2) +r%2Fs+=+8%2F7+
(2) +1920%2F1680+=+8%2F7+
(2) +7%2A1920+=+8%2A1680+
(2) +13440+=+13440+
OK