Word problem: salary and percent increases/decreases

[gio]

Hello Everyone,

I am currently working on this problem, but it is very confusing. I hope you can help me. Thank you in advance.
This is the problem:

You are going to get a pay rais and a pay cut.

a) Your salary is first increased by 15% then this new amount is cut by 15%. What percent of your original salary is this final salary?
b) Your salary is first cut by 15%. Then, this new amount is increased by 15%. What percent of your original salary is this final salary?
c) If your salary were cut by 15%, what percent raise would you need to get back to your original salary? Round to the nearest hundredth of a percent.
d) If you got a raise of 15%, what percent pay cut could you take and still make your original salary? Round to the nearest hundredth of a percent.

Once again thank you in advance. I will really appreciated it.

 

[Loren]

Re: Word problem

a) Your salary is first increased by 15% then this new amount is cut by 15%. What percent of your original salary is this final salary?

Let's try some real numbers in there and see what happens.

Say your salary is $200.
$200 increased by 15% is 200+.15(200) = 200 + 30 = $230
$230 cut by 15% is 230 - .15(230) = 230 - 34.50 = $195.50

Now, what percent of $200 is $195.50? That would be 195.50 is what percent of 200. 195.50/200=.9775. Therefore, the final salary is 97.75% of the original salary.

Use some other numbers and see if you get the same result. Then, you can take the next step by calling your first salary x. New salary would be x+.15x or 1.15x. You can take it from there???

 

[gio]

Re: Word problem

Hi Loren,

Thank you for helping in this problem. Now, my question is in part c), how come 15% is not needed to get back to the original salary if 15% was cut? Same happens to part d). I hope you can help me on this. I really appreciate your help. Thank you

 

[Mrspi]

Hello Everyone,


c) If your salary were cut by 15%, what percent raise would you need to get back to your original salary? Round to the nearest hundredth of a percent.
d) If you got a raise of 15%, what percent pay cut could you take and still make your original salary? Round to the nearest hundredth of a percent.

Once again thank you in advance. I will really appreciated it.

For part c, take a simple example. Suppose you start with a salary of $100. Now, if you receive a 15% cut, you'll be getting (100% - 15%) or 85% of $100 for your new salary. Your new salary will be $85.

How much of an increase would it take to get back to the original $100? You'd need to receive an additional $15. And what percent is 15 of 85?

15 = what percent of 85

15/85 = x/100

85x = 1500
x = 17.65 (rounded to the nearest hundredth)

So, you would need a raise of 17.65%.

You can use a similar approach for part d.

 

[Deleted member 4993]

Percentage calculation is done through division - we call the divisor (denominator) the base.

In your two calculations - the numerator remains the same(15) - but the base is canging (100 & 85)

 

[gio]

Guys,

I really appreciate your help. You all are very helpful thank you so much!!