单选题
A large flower arrangement contains 3 types of flowers: carnations, lilies, and roses. Of all the flowers in the arrangement, 1/2 are carnations, 1/3 are lilies, and 1/6 are roses. The total price of which of the 3 types of flowers in the arrangement is the greatest?(1) The prices per flower for carnations, lilies, and roses are in the ratio 1:3:4, respectively. (2) The price of one rose is $0. 75 more than the price of one carnation, and the price of one rose is $0. 25 more than the price of one lily.
【正确答案】
A
【答案解析】Let T be the total number of flowers, and let $C, $L，and $R be the cost, respectively, of one carnation, one lily, and one rose.(1) We are given that L = 3C (because C:L is 1:3) and R = AC (because C:R is 1:4). The table below shows the total price for each type of flower.
From the table it is clear that lilies have the greatest total cost; SUFFICIENT.(2) We are given that R = 0.75 + C and R = 0.25 + L. To simplify matters, we can use these equations to express each of the variables C, L, and R in terms of a single fixed variable, for example, C= R- 3/4 and L = R-1/4. This will allow us to replace all appearances of C, L, and R with appearances of R only, thereby reducing by two the number of variables that have to be dealt with. The table below shows, for two values of T and R， the total price for each type of flower.
From the table it is clear that lilies have the greatest total cost; SUFFICIENT.(2) We are given that R = 0.75 + C and R = 0.25 + L. To simplify matters, we can use these equations to express each of the variables C, L, and R in terms of a single fixed variable, for example, C= R- 3/4 and L = R-1/4. This will allow us to replace all appearances of C, L, and R with appearances of R only, thereby reducing by two the number of variables that have to be dealt with. The table below shows, for two values of T and R， the total price for each type of flower.