[問題]gwd-4-Q10

[小紅豆]

Q10: c
A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?
(1)x = 3Y/4
(2)The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.


我選了D .....
答案是C

[agk99]

第一次兼數學版，請多指教

利息一定是由金額乘上利率，這一題要問你利率多少
那麼你就得知道金額除上利息，才能得知利率，而題目也己經給你了金額與總利息的數值
但條件一只有告訴你利率的比率，這代表有無限可能(因為是二元一次方程式，答案有無限多)
條件二也是給你利息的比率，還是有無限可能(理由同上)
但兩條件合併，就可以逼出確切的利率

[Rusu]

1.還是有兩個變數..A*3Y/4+(60000-A)*Y=4080
2.得3*(60000-A)Y=2AX
1+2得A=40000, Y=0.0816,X=.....考試時不用算出來

[Rusu]

1.還是有兩個變數..A*3Y/4+(60000-A)*Y=4080
2.得3*(60000-A)Y=2AX
1+2得A=40000, Y=0.0816,X=.....考試時不用算出來

哈哈..沒看到agk大哥已解....慢了一步

[小紅豆]

感動......謝謝你們
.................. 以後也請多多指較

[faithful]

(2)The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

請問，為什麼條件二不能單獨充分？

題目已知利息總金額$4,080，條件二知道個別利息金額的比例。
$4,080 * 3/5 = $2,448
$2,448 = $60,000 * X
解一元一次方程式後，即可得知X。

懇請高人火速指點，再過兩週左右即將應考，感激不盡。

[faithful]

算了！
當我在耍白痴，我想到原因了。>_<

[dorisdi]

agk99 發表於: 2005-01-30 15:25 文章主題: Re: [問題]gwd-4-Q10

條件二也是給你利息的比率，還是有無限可能(理由同上)
但兩條件合併，就可以逼出確切的利率

(2)The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.
----------------------------------------------------------

我對條件二的解讀是
投資X%的金額對投資Y%的金額比是3:2
而不是利息比

請問大家的看法?

[Emilyh]

[quote]
1.還是有兩個變數..A*3Y/4+(60000-A)*Y=4080
2.得3*(60000-A)Y=2AX
1+2得A=40000, Y=0.0816,X=.....考試時不用算出來

我自己在算的時候，一直算不出來，請問有人可以把1+2然後算出A,Y的過程列出來嗎?

我已經算出來了，不好意思..

[piyopiyo]

I chose B.

According to condition (2), the total earned interest out of this $60,000 is $4080. And the ratio of the interest genearted by x% and y% is 3:2

Therefore, interest generated by x% is $4080*(3/5).
Then, $60,000*x% = $4080*(3/5)

So, Ans. is B.

What do u think?

[orange0828]

I chose B.

According to condition (2), the total earned interest out of this $60,000 is $4080. And the ratio of the interest genearted by x% and y% is 3:2

Therefore, interest generated by x% is $4080*(3/5).
Then, $60,000*x% = $4080*(3/5)

So, Ans. is B.

What do u think?

4080 = A*X%+B*Y%
$4080*(3/5)=A*X% 還是無法得出X%
我想應該是這個樣子吧
所以ANS=C

[chris8888]

我想補充說明 :

(2)The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

所以是利息賺到的錢的比例, 不是利息相比.

另外這一題若不解到最後可以縮短考試時間, 但是ETS, 常常有時候當你解出來時, 他是兩個答案, 這時候還是錯, 會變成E, 所以真是一個思索