Mathe F1 難題

2012-01-17 6:40 am

1)Five years ago,Mr Chan deposited $50000 in bank A at an interest rate of 5% p.a. This year,Mr Chan deposits the amount received from Bank A in Bank B.If simple interest is calculated in both cases,

1a) what is the amount that Mr Chan receives from Bank A?

1b)Mr Chan receives the simple interest $15000 from Bank B after four years.
i)Find the interest rate per annum offered by Bank B.

ii) He deposits the amount received from Bank B in Bank C at an interest rate of 6.5% p.a. simple interest.How long will it take for the amount to become $117800?

2)if a packet of sweets is distributed evenly among 10 children,1 sweet will be left.If the same packet of sweets is distributed evenly among 12 children, the number of sweets that each child gets will be 3 less than before, and 9 sweets will be left.Find the number of sweets in the packet.

要完整解釋,詳細列式及步驟,不要跳過太多步驟

更新1:

1b ii 可以用方程嗎,及解釋

回答 (1)

wanszeto

2012-01-17 8:37 am

✔ 最佳答案

1a)
A = P(1 + n x R%)

Amount that Mr Chan receives from Bank A
= $50000 x (1 + 5 x 5%)
= $62500

1b) i)
I = P x n x R%
Hence R% = I/(P x n)

Interest rate
= [15000 / (62500 x 4)] x 100%
= 6%

1b) ii)
A = P(1 + n x R%)
A = P + P x n x R%
A - P = P x n x R%
Hence n= (A - P)/(P x R%)

No. of years
= [117800 - (62500 + 15000)] / [(62500 + 15000) x 6.5%]
= 8 (years)

2)
Let n be the number of sweets that each child gets when the packet of sweets isdistributed evenly among 10 children.

Number of sweets :
10n + 1 = 12(n - 3) + 9
10n + 1 = 12n - 36 + 9
2n = 28
n = 14

Hence, number of sweets in the packet
= 10 x 14 + 1
= 141

參考: wanszeto

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