Question

数学题，急求解答！先谢谢大家了，要说明方法，如果是英文的更好

1. At a party, 65 bowls were used to serve hot food: soup, rice and chicken. Each
bowl of rice served two guests, each bowl of soup served three guests, and each
bowl of chicken served four guests. How many guests were present at the dinner?
(We assume that all guests ate the full meal: soup, rice and chicken)
2. Bill Gates offers you a job for one month. He gives you a choice of one of the
two possible salary schemes: you can receive either a sum of $10,000 a day for
each day of the month (including weekends), or you will receive your payment
according to the following formula: 1 cent for the first day, 2 cents for the second
day, 4 cents for the third day, 8 cents for the fourth day etc. Which payment
would you choose and why?
3. On Monday, a FedEx delivery truck made the following successive trips, starting
in the morning from its base: 145 km to the east, then 175 km to the west, then 20
km to the west, then 43 km to the east.
Illustrate the trips of the truck on the number line (where will you put the base?).
Use your diagram (and the calculations required) to answer the questions below:
(a) At the end of the fourth trip, is the truck east or west of his base?
(b) How far must the truck drive to return to its base?
4. Number trick:
(a) Think of a number between 1 and 50. Write it down. Double this number. Add 20
to the result. Now add 6. Subtract 17. Subtract 9. Divide by 2. What is the
result? Try it again, starting with another number between 1 and 50. What is your
answer now?
(b) Will this procedure always work? Let’s prove it! Starting with “Let n = the
number between 1 and 50”, write a single expression for the operations described
in (a) (in terms of n), remembering order of operations. Remember to be
mathematically correct in everything you write! Now simplify that expression and
comment on what you find.

Answer 1

1 每个人都要喝soup, rice and chicken,用(1/2+1/3+1/4)=13/12个碗,65个碗可供:65*12/13=60个人用
2 第1种的收入是10000*30=300000元
第2种是等比数列的和=(2^30-1)/100 ,(首项是1,公比是2,除100是把分化为元),结果远远大于第1种,所以选第2种
3 往东用+号表示,往西用-号表示:
+145-175-20+43=-7
a 在西面
b 7KM
4 假设你想的数是X,Double this number (2X). Add 20
to the result. Now add 6. (2X+20+6=2X+26). Subtract 17. Subtract 9.(2X+26-17-9=2X). Divide by 2.(2X/2=X) . the Result IS X (THE SAME)

Answer 2

1.x+y+z=65;3x=2y;x=2z;4y=3z方程组求解。x：bowls of rice；y：bowls of soup；z：bowls of chicken .So the number of guests is double x.
2.以2为比值的等比数列求和。首项为1，共30项。结果cents转化为dollers也比300000大，故，选第二个方案。
3.a）west
b）12km
4.a）itself
b）double n，then add 4.5
权作参考。

Answer 3

呵呵。...现在手头没笔...先把翻译的发上来吧..
1。在一次聚会上65碗，是用来提供热的食物：汤，米饭和鸡肉。每个
一碗饭担任两位客人，每一碗汤担任三位客人，每
鸡碗担任四个客人。有多少嘉宾出席了晚宴？
（我们假定所有的客人吃全餐：汤，米饭和鸡肉）
2。比尔盖茨为您提供了1个月工作。他给你一个选择的一
两个可能的薪金方案：您可以接收到10,000元，每天款额
每一个月（包括周末日），或者您将收到您的付款
根据以下公式计算：1美分的第一天，2美分第二
一天，4美分的第三天，8美分，第四天等，这些付款
你会选择，为什么？
3。周一，联邦快递货运卡车作出以下连续旅行，出发
在从基地：145公里，东，然后175公里，西，那么20日上午
公里到西部，然后43公里，东。
说明对数线车的车次（如你把基地？）。
使用您的图表（和计算要求）回答下列问题：
（一）在第四次访问结束时，是卡车东部或西部的基地？
（二）必须有多大的卡车驱动器返回基地？
4。编号技巧：
（1）想象一个介于1和50之间。它写下来。双数。添加20
到结果。现在添加6。减去17。减去9。除以2。什么是
结果呢？再试一次，另有1到50号开始。什么是您
答案呢？
（b）将这个过程始终的工作？让我们证明这一点！开始“的设n =
1至50号“，写一个单一的行动表达描述
（一）（以n项），记忆秩序的行动。记得要
数学纠正你写的一切！现在简化的表达和
评论你找到。