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Question

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*3) Last year, the salaries of Cindy and Katy were the same. This year, Katy's salary is increased by 8% while Cindy's salary is decreased by $300.
(a) Suppose Katy's salary is $8100 now.
(i) What was Katy's salary last year?
(ii) What is the percentage decrease in Cindy's salary?
(b) Suppose the difference between their present salaries is $1100. Find their salaries last year.

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Answer 1

*3) Last year, the salaries of Cindy and Katy were the same. This year, Katy's salary is increased by 8% while Cindy's salary is decreased by $300.
(a) Suppose Katy's salary is $8100 now.
(i) What was Katy's salary last year?
Katy's salary last year
= $8100 / (1 + 8%)
= $8100 / 108%
= $8100 / 1.08
= $7500
=============================================
(ii) What is the percentage decrease in Cindy's salary?
Cindy's salary last year
= Katy's salary last year
= $7500
Percentage decrease in Cindy's salary
= $300/$7500 * 100%
= 4%
=============================================
(b) Suppose the difference between their present salaries is $1100. Find their salaries last year.
Let their salary last yeara be $x.
Katy's salary this year
= $x (1 + 8%)
= $x (108%)
= $1.08x
Cindy's salary this year
= $x - $300
= $(x-300)
As the difference is $1100, so
$1.08x - $(x-300) = $1100
1.08x - x + 300 = 1100
0.08x = 800
x = 10000
So their salary last year is $10000.

2007-01-11 17:47:04 補充：
小小補充：這條題目 (a)(i), (a)(ii) 和 (b) 是沒有關係的。因為 (a) 和 (b) 開首都說明「Suppose...」如果將它們一併考慮就會混亂了。

Answer 2

a)(i) Let x be the salary of Katy last year.
x*(1+8%)=8100
x*(108%)=8100
108x =810000
x=7500
a)(ii) Let x% be the percentage decrease in Cindy's salary.
7500*x%=300
7500x =30000
x=4
The percentage decrease in Cindy's salary is 4.
b) Let x be the salary of Katy last year and,
y be the salary of Cindy last year.
x=y....1
x*(1+8%)-1100=y-300....2
Substitute 1 into 2
y*(1+8%)-1100=y-300
y*108%-1100=y-300
y*108% =y+800
108y =100y+80000
100y+8y=100y+80000
8y=80000
y=10000
The salaries of katy was 10000 and that of Cindy was also 10000 last year.

Answer 3

a)
i) $7,500
ii) 4%
b)
$10,000

Answer 4

(a)
(i)
Let x be the salary of Katy last year
x + ( x * 8%) = 8100
x (1+8%) = 8100
x = 7500
Ans: Katy's salary last year was $7500

(ii)
Let y be the decrease in Cindy's salary
7500 - (7500 * y%) = 300
7500 * y% = 7200
y% = 0.96
y = 4%
Ans: The decrease in Cindy's salary is 4%

Answer 5

a)1) 8100 除 (1+8%) =7500
a)2) 300 / 7500 x100% =4%
b) let y be the respective salaries last year
y(1+8%) - y (1-4%) = 1100
1.08y -0.96y =1100
0.12y=1100
y=9166.67(corr to 2dp)
respective salaries=9166.67
total = 18333.33(corr to 2dp)