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Question 515748: You are buying flowers to hand out at a school dance. Roses cost $30 for a dozen but cost more if bought individually. With the money you have, you can buy 7 dozen and 4 single roses, or 64 single roses. How much is one rose? How much money do you have?
Thanks so much for your help. This is a word problem on my homework and i don't understand so i would really appreciate it.:)
Answer by drcole(72)   (Show Source):
You can put this solution on YOUR website! Let m represent the amount of money that you have (in dollars). Let x represent the cost of a single rose (also in dollars). We are told that, with the amount of money you have, you can buy 64 single roses. Since a single rose costs x dollars, 64 single roses would cost 64x dollars, which we know is equal to the amount of money you have (we are assuming here that you don't get change back). This gives us an algebraic equation:
64x = m
We are also told that, with the money that you have, you could buy seven dozen roses, at $30 a dozen, plus four single roses. At $30 a dozen, seven dozen roses would cost (7)(3) = 210 dollars. At x dollars per single rose, four single roses would cost 4x dollars. Together those dollar amounts equal the money that you have, m dollars, so we can set up a second algebraic equation:
210 + 4x = m
Now we have two equations in two unknowns, both of which are solved for m. Since m is equal to both 64x and 210 + 4x, we can set these two expressions equal to each other, yielding a single equation in x:
64x = 210 + 4x
Now we solve for x:
60x = 210 (subtract 4x from both sides)
x = 3.5 (divide both sides by 60)
So we get that each single rose costs $3.50. To get the amount of money we have, we now substitute back 3.5 for x in the first equation:
64x = m
64(3.5) = m (substituting back 3.5 for x)
224 = m
So we have 224 dollars for buying flowers to hand out at the school dance. Does this make sense? At $3.50 per single rose, 64 single roses would cost 64(3.50) = 224 dollars, so that works. At $30 per dozen roses and $3.50 per single rose, seven dozen roses and 4 single roses would cost
7(30) + 4(3.50) = 210 + 14 = 224 dollars
which is the same amount as we figured out, so that also works. So we have the correct answer.
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