Leo has a salary of 馃挿 120000. Calculate his new salary if it is increased by x% & decreased by x%. [I Like Mathematics]
The answer is: 120000(1 - x^2/10^4)
Please explain the steps.
Please explain the steps.
This page is a permanent link to the reply below and its nested replies. See all post replies 禄
Riemann 路 31-35, M
@FrozenWasteland Steps?
FrozenWasteland 路 61-69, M
@Riemann
Current salary is 120000.
x% of that is, by definition 120000 * x / 100.
After the raise, salary is 120000 + 120000 * x /100.
Or, factoring out the 120000, we get 120000 * (1 + x / 100).
Then do a similar thing for the x% decrease.
The rest is just a bit of algebra.
What part is giving you issues?
Current salary is 120000.
x% of that is, by definition 120000 * x / 100.
After the raise, salary is 120000 + 120000 * x /100.
Or, factoring out the 120000, we get 120000 * (1 + x / 100).
Then do a similar thing for the x% decrease.
The rest is just a bit of algebra.
What part is giving you issues?
Riemann 路 31-35, M
@FrozenWasteland Could you please explain the factoring part?
FrozenWasteland 路 61-69, M
@Riemann ok. Basically we're going to multiply the whole thing by 120000 and then divide by 120000. Maybe that will be illustrative.start with:
y = 120000 + 120000 * x / 100
Do the multiply and divide:
y = 120000 * (120000 + 120000 * x / 100) / 120000
Now distribute the division over the two terms in the parentheses.
y = 120000 * (120000 / 120000 + 120000 * x / 100 / 120000)
Clearly 120000/120000 is 1 and 120000 * x / 100 / 120000 is just x / 100.
So 120000 + 120000 * x / 100 equals 120000 * (1 + x / 100)
Does that help or make it worse?
y = 120000 + 120000 * x / 100
Do the multiply and divide:
y = 120000 * (120000 + 120000 * x / 100) / 120000
Now distribute the division over the two terms in the parentheses.
y = 120000 * (120000 / 120000 + 120000 * x / 100 / 120000)
Clearly 120000/120000 is 1 and 120000 * x / 100 / 120000 is just x / 100.
So 120000 + 120000 * x / 100 equals 120000 * (1 + x / 100)
Does that help or make it worse?
Riemann 路 31-35, M
FrozenWasteland 路 61-69, M
@Riemann That's correct. you need to decrease x% from 120000 * (1 + x/100). So you get:
120000 * (1 + x/100) * (1 - x/100)
The decrease is always bigger than the increase was (in dollars, not percentage) because it's the same percentage of a larger number. Think of a 100% increase followed by a 100% decrease -- whatever you started with, the end result is 0.
120000 * (1 + x/100) * (1 - x/100)
The decrease is always bigger than the increase was (in dollars, not percentage) because it's the same percentage of a larger number. Think of a 100% increase followed by a 100% decrease -- whatever you started with, the end result is 0.