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34) if there are x red roses and y yellow roses and each rose
costs $8 and each yellow rose costs $3,what is the cost of red roses in a bouquet of $80.
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Assuming you meant to say each RED rose costs $8...
You have 8x + 3y = 80. x and y have to be integers since you're not going to buy your lovely wife/mom/girlfriend a half of a rose. So now your just try out some numbers. If you buy one $8 rose, that leaves $72 for 24 yellow roses. So that's one possibility.
If you buy 2 red roses for $16, that leaves $64 dollars for 21.333 yellow roses. No good.
If you buy 3 red roses for $18, that leaves $56 dollars for 18.666 yellow roses. No good.
If you buy 4 red roses for $24, that leaves $48 dollars for 16 yellow roses. Good.
Continue this and hopefully you'll pick up the pattern. You can buy the following bouquets for $80:
1 red and 24 yellow
4 red and 16 yellow
7 red and 8 yellow
10 red and 0 yellow
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