问题 解答题

我市某林场计划购买甲、乙两种树苗共800株,甲种树苗每株24元,乙种树苗每株30元.相关资料表明:甲、乙两种树苗的成活率分别为85%,90%.

(1)若购买这两种树苗共用去21000元,则甲、乙两种树苗各购买多少株?

(2)若要使这批树苗的总成活率不低于88%,则甲种树苗至多购买多少株?

(3)在(2)的条件下,应如何选购树苗,使购买树苗的费用最低,并求出最低费用.

答案

(1)甲种500株,乙种300株;(2)320株;(3)甲种320株,乙种480株,22080元

题目分析:(1)根据关键描述语“购买甲、乙两种树苗共800株,”和“购买两种树苗共用21000元”,列出方程组求解.

(2)先找到关键描述语“这批树苗的成活率不低于88%”,进而找到所求的量的等量关系,列出不等式求出甲种树苗的取值范围.

(3)再根据题意列出购买两种树苗的费用之和与甲种树苗的函数关系式,根据一次函数的特征求出最低费用.

(1)设购买甲种树苗x株,则乙种树苗y株,由题意得:

答:购买甲种树苗500株,乙种树苗300株;

(2)设甲种树苗购买z株,由题意得:

85%z+90%(800-z)≥800×88%,

解得z≤320.

答:甲种树苗至多购买320株;

3)设购买两种树苗的费用之和为m,则m=24z+30(800-z)=24000-6z,

在此函数中,m随z的增大而减小

所以当z=320时,m取得最小值,其最小值为24000-6×320=22080元

答:购买甲种树苗320株,乙种树苗480株,即可满足这批树苗的成活率不低于88%,又使购买树苗的费用最低,其最低费用为22080元.

点评:将现实生活中的事件与数学思想联系起来,读懂题列出不等式关系式即可求解.本题难点是求这批树苗的成活率不低于88%时,甲种树苗的取值范围.

单项选择题
单项选择题

Although there are many skillful Braille readers, thousands of other blind people find it difficult to learn that system. They are thereby shut (1) from the world of books and newspapers, having to (2) on friends to read aloud to them.

A young scientist named Raymond Kurzweil has now designed a computer which is a major (3) in providing aid to the (4) .His machine, Cyclops, has a camera that (5) any page, interprets the print into sounds, and then delivers them orally in a robot-like (6) through a speaker. By pressing the appropriate buttons (7) Cyclops’s keyboard, a blind person can "read" any (8) document in the English language.

This remarkable invention represents a tremendous (9) forward in the education of the handicapped. At present, Cyclops costs $ 50,000. (10) , Mr. Kurzweil and his associates are preparing a smaller (11) improved version that will sell (12) less than half that price. Within a few years, Kurzweil (13) the price range will be low enough for every school and library to (14) one. Michael Hingson, Director of the National Federation for the Blind, hopes that (15) will be able to buy home (16) of Cyclops for the price of a good television set.

Mr. Hingson’s organization purchased five machines and is now testing them in Maryland, Colorado, Iowa, California, and New York. Blind people have been (17) in those tests, making lots of (18) suggestions to the engineers who helped to produce Cyclops.

"This is the first time that blind people have ever done individual studies (19) a product was put on the market," Hingson said. "Most manufacturers believed that having the blind help the blind was like telling disabled people to teach other disabled people. In that (20) , the manufacturers have been the blind ones.

14()

A.settle

B.own

C.invest

D.retain