问题 解答题
某市蔬菜基地有一批蔬菜若干吨,有三种销售方式,利润如下表
销售方式
市场直接销售
粗加工销售
精加工销售
每吨获利(万 元)
0.1
0.45
0.75
已知加工能力如下:若蔬菜总量再增加20吨,粗加工刚好10天全部加工完.若蔬菜总量减少20吨,精加工刚好20天全部加工完,且精加工比粗加工每天少加工10吨,又精加工和粗加工不能同时进行,而受季节限制,基地必须要15天(含15天)内全部加工或销售,为此基地特制定了三种方案:①尽可能多的精加工,来不及加工的在市场上直接销售,②全部粗加工,③将一部分精加工,其余蔬菜粗加工,且刚好15天完成.
解答下列问题:(1)求基地这批蔬菜有多少吨?(2)哪种方案获利最多?最多为多少万元?
答案

基地这批蔬菜有140吨;方案③获利最多,最多为81万元

题目分析:解:(1)设基地这批蔬菜有x吨,则

去分母得2(x+20)-200=x-20整理得2x+40-200=x-20  

所以x=140

∴基地这批蔬菜有140吨.

(2)每天精加工的吨数为:;每天粗加工的吨数为:

方案①:6×15×0.75+(140-6×15)×0.1=72.5万元.

方案②:140×0.45=63万元.

方案③:设精加工a天,精加工(15-a)天,则6a+16(15-a)=140,

6a+240-16a=140,-10a=-100,a=10

∴15-a=15-10=5,∴获利:10×6×0.75+5×16×0.45=81万元

∵81>72.5>63,∴方案③获利最多,最多为81万元.

点评:本题难度中等,主要考查学生对一元一次方程应用解决实际问题的能力,为中考常考题型,要求学生牢固掌握解题技巧。做方案分析时需要建立所有标准模型范围,代入求值。

单项选择题
阅读理解

When Boris left school, he could not find a job. He tried hard and pestered (纠缠) his relatives, but they had problems of their own. He answered advertisements until he could not afford to buy any more stamps. Boris grew annoyed, then depressed, then a little hardened. Still he went on trying and still he failed. He began to think that he had no future at all.

“Why don't you start your own business?” one of his uncles told him. “The world is a money-locker. You'd better find a way of opening it.”

“But what can I do?”

“Get out and have a look round.” advised his uncle in a vague sort of way. “See what people want; then give it to them, and they will pay for it.”

Boris began to cycle around the town and found a suitable piece of a waste ground in the end. Then he set up his business as a cycle repairer. He worked hard, made friends with his customers and gradually managed to build up his goodwill and profit. A few months later, he found that he had more work than he could deal with by himself. He found a number of empty shops but they were all no good: in the wrong position, too expensive or with some other snag(障碍). But at long last, he managed to find an empty shop on a new estate where there were plenty of customers but no competition.

Boris and his assistant taught themselves how to repair scooters and motor-cycles. Slowly but surely the profits increased and the business developed. At last, Boris had managed to open the money-locker and found bank notes and gold coins inside.

小题1:Which of the following best describes Boris' job hunting experience?

A.Surprising.

B.Encouraging.

C.Boring.

D.Disappointing.小题2:Which of the following would be the best title for the passage?

A.Goodwill is the key to success

B.The world is a money-locker

C.No education, no future

D.Difficulty of starting a small business小题3:Boris started his career by       .

A.repairing cycles

B.developing a waste ground

C.cycling around the town

D.buying empty shops小题4:Boris finally chose an empty shop on a new estate because       .

A.it was not so expensive

B.he had a lot of old customers there

C.there were good opportunities there

D.he could make good use of his skills there小题5:We can infer from the last paragraph that Boris     .

A.still couldn't make good profits

B.found a lot of gold coins by accident

C.set off in a successful career

D.had great difficulty running his business