Roses can be purchased individually for $4.30, one dozen for

$50 deals is the best. 650/50=13 two dozen roses

10*24 = 240 roses
3*24 = 72 roses

Total is 312 (close to 318) answer is assumed C

One rose for 4.30$
12 for 36$ i.e., 1 rose for 3$
24 for 50$ i.e., 1 rose for 2$ approx...........cheapest price

So we need greatest number of roses, we need to buy maximum for less price i.e., we should buy them at 24 for 50$ as much as we can.
Given,
680$=650$(multiple of 50$) + 30$
=50$(13)(multiple of 50$ i.e., number of 24 rose sets for 50$) +30$(we can only buy roses individually with this price.)

For 650$,
since we get 24 roses for 50$ and we get total such 13 sets of roses whereas each set has 24 roses i.e.,
\(13*24=(10+3)24=240+72=312 roses\)
for 650$ we can buy maximum 312 roses

For 30$,
at individual price of 4.3$, we can buy \(\frac{30}{4.3}\)i.e., 6 roses at maximum.

So in total the greatest number of roses we can buy for 680$ is 312+6=318 roses

I can understand that C is the answer. However, I disagree with the word "for $680?". Such word is not as same as "with $680" That means we have to find the precise cost.

chesstitans , I am not sure I understand your distinction. It seems as if you are saying that the phrase "for $X" means only something such as, "I bought three dresses for $887.93."

Where did your interpretation(s) come from? Can you give an example?

In English, when given an amount of money, a price per item, and a question that asks us to find the number of items, "with $680" and "for $680" mean the same thing. They mean, "How many roses will $680 allow you to buy?"

$680 is the upper limit. You do not have to spend all the money, but you cannot spend more.

Does that make sense, or have I misunderstood you?

Since the $50 one are the cheapest on per unit basis, we will try to buy maximum of such roses first till the point we can then move on to buy the $36 ones and so on.

[680/50] = 13 , [] stands for the greatest integer less than or equal to that number.

Since, (680-50*13)=30

Also, [30/4.3] = 6 , [] stands for the greatest integer less than or equal to that number.

So max. no. of roses that can be purchased = 13*24 + 6 =318

Note first that the cheapest price per rose is obtained by buying a 2-dozen bouquet. Thus, we want to buy as many 2-dozen bouquets as possible.

Since 650/50 = 13, 13 x 24 = 312 roses can be purchased for 650 dollars when buying them 2 dozen at a time.

With the remaining 30 dollars, 6 more roses can be purchased, for a total of 318 roses.

Answer: C

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