Question

Leo has a salary of $120,000. Calculate his new salary if it is :
(a) increased by 10%, then decreased by 10%
(b) increased by x%, then decreased by x%

Please help!! Thanks!~

Answer 1

(a) New salary is $120,000 * 1.1 * 0.9 = you can calculate

Answer 2

hi :)
did u get that ?
or need some more explanation ?

Answer 3

The solution to (a) can be put in more detail as follows:
\[New\ salary=$120,000\times(1+\frac{10}{100})\times(1-\frac{10}{100})\]

Answer 4

I got part (a) --Thanks @kropot72--, but I don't know how to get the answer for part (b).
According to my textbook, the answer for part (b) is $120,000 ( 1- x^2/10^4)
Please explain!!

Answer 5

(b) If you look at the detailed posting of the solution to (a)
\[New\ salary=$120,000\times(1+\frac{10}{100})\times(1-\frac{10}{100})\]
and plug in x instead of 10 we get
\[New\ salary=$120,000\times(1+\frac{x}{100})(1-\frac{x}{100})\]
Can you see that the two terms in x are the factorization of the difference of two squares?

Answer 6

Yes~

Answer 7

So when we multiply out those two terms in x we get
\[1-(\frac{x}{100})^{2}\]

Answer 8

lets take it part by part
for any quantity say, A,
10% of it is A*10/100
x% of A is A*x/100

If A increased by 10% means A + 10% of A = A (1+ 10/100)
If A increased by x% means A + x% of A = A (1+ x/100)

thats the basic thing, you can apply this repeatedly in your problem

Answer 9

\[1-(\frac{x}{100})^{2}=(1-\frac{x ^{2}}{10^{4}})\]

Answer 10

for decrease, you just use negative sign,
A decreased by x% = A (1-x/100)

Answer 11

Oh, I get it now! Thanks a lot @kropot72 and @hartnn :)

Answer 12

You're welcome :)