Need help!!!

麦兜woo

Q19: E

This year Henry will save a certain amount of his income, and he will spend the rest.  Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend.  In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?



A.1／(r+2)

B.1／(2r+2)

C.1／(3r+2)

D.1／(r+3)

E.1／(2r+3)
答案选E，可是我做出的答案怎么是(1-2r)／3

2.How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?



A. 15

B. 16

C. 17

D. 18

E. 19

答案选C，很不解，怀疑答案错了，我选B，from 1 to 50,比3的倍数多1的数一共只有16个啊,求证

3.A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly.  Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively.  What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?



A. 20

B. 36

C. 48

D. 60

E. 84

选C，不知道怎么来的？

麦兜woo

UP

sdcar2010

This year: Money spent: $A; money saved $B
Next year: Money spent: $B(1 + r)

Since money spent next year is only half of money spent last year, then B(1 + r) = A/2 or A = 2B (1 + r)

Fraction of income saved this year = B / (A + B) = B / [2B (1 + r) + B] = 1/(2r + 3)

sdcar2010

2.How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?

You forgot the number 1.

sdcar2010

A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly.  Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively.  What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

Based on the info above, an increase of (24-6) = 18 on the R-scale corresponds to an increase of (60-30) = 30 on the S-scale.  Therefore, an increase of 6 on the R-scale corresponds to an increase of 10 on the S-scale. So an increase of 6 * 4 = 24 on the R-scale corresponds to an increase of 10 * 4 = 40 on the S-scale.  Then, on the R-scale (24 + 24) = 48 should correspond to (60 + 40) = 100 on the S-scale

麦兜woo

2.How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?

You forgot the number 1.

-- by 会员 sdcar2010 (2010/12/3 10:16:19)

is the remainder 1 1when 1is divided by 3? I cannot see

麦兜woo

A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly.  Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively.  What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

Based on the info above, an increase of (24-6) on the R-scale corresponds to an increase of (60-30) on the S-scale.  Therefore, an increase of 6 on the R-scale corresponds to an increase of 10 on the S-scale. So an increase of 24 on the R-scale corresponds to an increase of 40 on the S-scale.  Then, on the R-scale 24 + 24 = 48 should correspond to 100 (60 + 40) on the S-scale

-- by 会员 sdcar2010 (2010/12/3 10:20:49)

sorry，我还是不理解，你能再详述下吗，最好用中文，原谅我的水平~~

luweiluwei

给楼主一个简便容易理解的方法，牛牛的方法不是很好理解，但是原理和下面的方法一样

设两个方程式
根据第一个条件 6=A+30B
根据第二个条件 24=A+60B
得出 B=0.6 A=-12

联立方程 R=-12+0.6S
求的问题是当S=100时， R的值 为 48

麦兜woo

给楼主一个简便容易理解的方法，牛牛的方法不是很好理解，但是原理和下面的方法一样

设两个方程式
根据第一个条件 6=A+30B
根据第二个条件 24=A+60B
得出 B=0.6 A=-12

联立方程 R=-12+0.6S
求的问题是当S=100时， R的值 为 48

-- by 会员 luweiluwei (2010/12/3 11:39:34)

I got it, thanks ~~

xuhui27

A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly.  Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively.  What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

Based on the info above, an increase of (24-6) = 18 on the R-scale corresponds to an increase of (60-30) = 30 on the S-scale.  Therefore, an increase of 6 on the R-scale corresponds to an increase of 10 on the S-scale. So an increase of 6 * 4 = 24 on the R-scale corresponds to an increase of 10 * 4 = 40 on the S-scale.  Then, on the R-scale (24 + 24) = 48 should correspond to (60 + 40) = 100 on the S-scale

-- by 会员 sdcar2010 (2010/12/3 10:20:49)

牛牛的方法很赞！ 纯玩艺术的。。。赞赞！


我之前用的办法是：
因为题目已经说了两个是linearly相关的。
用线性方程


6a+b=30
24a+b=60


解出a ， b的值，然后带入  Xa+b=100 得出x是48。。。