陈向东 真题150(142/146) 两道复杂应用题

1 A home owner must pick between paint A, which costs 6 dollar per liter, and paint B, which costs 4.5 dollar per liter. Paint B takes one-third longer to apply than paint A. If the home owner must pay the cost of labor at the rate of 36 dollar per hour, which of the two paints will be cheaper to apply?

(1) the ratio of the area covered by one liter of paint A to the area covered by paint B is 4:3

(2) Paint A will require 40 liters of paint and 100 hours of labor

2 In a certain law firm there are five senior partners and five junior partners and all senior partners receive bonuses greater than those of the junior partner. Does senior partner J receive the largest bonus of the lawyers at the firm?

(1) J receives a bonus greater than twice the average bonus for all the senior partners

(2) All partners receive some bonus, and Mr. J receives five times the average given to all the partners

答案见二楼

1题观点为 （A/C）

2题（B）

恳请指教！

小算了一下。望指教。

1 A home owner must pick between paint A, which costs 6 dollar per liter, and paint B, which costs 4.5 dollar per liter. Paint B takes one-third longer to apply than paint A. If the home owner must pay the cost of labor at the rate of 36 dollar per hour, which of the two paints will be cheaper to apply?

(1) the ratio of the area covered by one liter of paint A to the area covered by paint B is 4:3

(2) Paint A will require 40 liters of paint and 100 hours of labor

我选C.

因为总的cost=paint的cost+labor的费用。（1）没提到粉刷时间==〉不充分

(1）（2）结合可算出AB各自要用的paint的量（由此算出各自用在paint上的cost)和分别用AB刷要用的时间。===〉充分。

2 In a certain law firm there are five senior partners and five junior partners and all senior partners receive bonuses greater than those of the junior partner. Does senior partner J receive the largest bonus of the lawyers at the firm?

(1) J receives a bonus greater than twice the average bonus for all the senior partners

(2) All partners receive some bonus, and Mr. J receives five times the average given to all the partners

我选B。

设五个senior的平均工资是A，五个junior的平均工资为B。

（1）J〉2A    分析：1。可能还有一个人的工资〉J。 其他三个senior的工资的和小于A。

                     2。也可能J是最高的。

（2）J= 1/2（5A+5B）    不可能还有人拿到〉1/2（5A+5B）的工资。因为十个人的工资总数为5A+5B。

RE ls

基本同意2楼的意思

还有没有人有其他的想法呢

我覺得這題選A.  算total cost 可以用以下的算式:

Total Cost = (Area / rate of work) * (cost of labor per hour ) + (amount of paint) * (cost of paint per liter)    

    (Area/rate of work) = # of hour of labor   paint A's rate is 4/3 of paint B's. 

Using (1), amount of paint A needed is 3/4 of paint B needed to paint the same area.

so if total Cost of A is  (Area/Rate) * ($36/Hr) + (# of Liter) * ($6/Liter)

then total cost of B is  (Area/ (3/4*Rate)) * ($36/Hr) + ((4/3)(# of Liter) * ($4.5/Liter)

                                = 4/3 (Area/Rate) * ($36/Hr) + (# of Liter)*($6/Liter)

=> Total cost B > total cost A.   (油漆錢相等, 工錢B比較多) 

不知道這樣思考有沒有漏洞,請指教

究竟这句话是什么意思呢？

怎么把它转换成数学语言呢？

我又想了一下,觉得2楼的也有点问题.就是LZ这话的问题,我觉得意思应该是用B涂的时间比用A涂的时间长1/3,也就是涂A用K小时,涂B用4/3K小时.这样的话,需要涂的总面积是一定的,1,2都是可以的.所以可能是D?

具体:

A  6/L     B 4.5/L    每升B比每升A多花1/3的时间    涂A用K小时,涂B用4/3K小时

ratio是4:3,而需要涂的总面积S一定,则用A涂需要S/4,用B涂需要S/3

则costA=S/4*6+S/4*k*36    costB=S/3+S/3*k*36

如果这句话的意思是用B的时间比用A多那么多,不管两个各用多少,道理是一样.

恳请指正!

开始同意6楼的观点 选择A 但综合了hsummer的观点

题目给定的条件如下 , 其中a,b,s为我设的未知数

要刷的总面积为S

A: $6/L, B: $4.5/L

A: aHRS/L, B:4/3aHRS/L, $36/HRS

在（1）的条件下，我们又得到这么一组关系， A: 4b/L, 即单位L可以粉刷的面积， B: 3b/L

继而我可以得到A的总成本为：s/4b * 6 + a * 36 =        1.5s/b+36a

                   B的总成本为：s/3b * 4.5 + 4/3a * 36 =1.5s/b +48a

显然上下一比B的成本高

在（2）的条件下，缺乏A,B单位L可以粉刷的面积的比例关系，不充分

大家的意思呢？