A few Maths question

Last year, the salaries of Cindy and Katy were the same. This year, This 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?
let Katy's salary last year is $y
y(1+8%)=8100
1.08y=8100
y=7500
Therefore, Katy's salary last year is $7500
(ii) What is the precentage decrease in Cindy's salary?
Cindy's salary last year is $7500
300/7500*100%
=4%
(b) Suppose the difference between their present salaries is $1100. Find their salaries last year.

Let both Cindy and Katy last year's salary be $z
z*(1+8%)-(z-300)=1100
1.08z-z+300=1100
0.08z=800
z=10000
Therefore, both Cindy and Katy last year's salary is $10000

Last year : c = k

This year : K = 1.08k
C = k -300
K = 8100
____________________________

1) 1.08 X k = 8100
k = 7500

2) (this year - last year ) / last year X 100%
therefore 300/k X100%
k = 3.7% (decrease)

b) | 1.08k - (k-300) | = 1100

1.08k-k+300 = 1100 -1.08k+k -300 +1100
0.08k=800 -0.08k= 1400
k = 10000 k= -17500 (therefore reject)


Get it?

(a) (i) Let $x be Katy's salary last year

X(1+8%) = 8100
X(1+0.08)=8100
1.08X =8100
X = 8100/1.08
X = 7500

so Katy's salary last year was $7500

(ii) Last year Cindy and Katy's salary were the same, so Cindy's salary last year was also $7500

Let y be the percentage decrease in Cindy's salary this year

7500* (1+y) = 7500+300
7500* (1+y) = 7800
7500 + 7500y =7800
7500y = 7800- 7500
7500y =300
y= 300/7500
y= 1/25
=0.04

so the percentage decrease is 0.04*100% = 4%