Maths question. Please help!?

Question

A teacher's salary increased from $58 842 pa to $62 373.50. Calculate his percentage pay rise.

Please help!! I'm a bit confused. I don't know which percentage to find. Please help, and can you please go through the question in clear, easy to understand steps and explain each step carefully? Thank you very much!!!

Why do you divide the difference by the previous salary? Im really confused? I was dividing the difference by the new salary.

Answer 1

Answer to additional information:

If you want to find the percentage of increase, you have to divide by what is being increased, also known as the original salary.

If you divide by the new salary, you will find the percentage of decrease, which will give you a different number entirely.

Answer 2

get the difference of the old and new, then divide it by the old to get the percentage of increase...
(62 373.50 - 58 842) / 58 842
or it could be expressed as this:
let x the % of increase
58 842 + 58 842x = 62 373.50
58 842x = 62 373.50 - 58 842
x = 3 531.50 / 58 842

why the old? It's because it's your base amount. You are looking for the increase from the old to new.

Answer 3

(62,373.50 - 58,842)/58,842 = .06 or 6%

Looking at it like this might make it easier to see. For the problem you want to know the percentage increase, so you know that the old salary increased by a amt. and gave you the new salary.

old salary + increase = new salary
58,842 + 3531.50 = 62,373.50

Now, you know the amt. but still no percent.

Look at it this way, you have an old salary, but you don't have your new salary unless you have the increase. This allows you to see that your increase had to be a percentage of you old salary. I mean, how can you have a percent of something you don't even have.

So now you know that the increase was a percentage of the old salary. *"percentage" is expressed as a decimal

(old salary)(percentage) = increase
(58,842)percentage) = increase

Now looking back at the problem earlier....
old salary + increase = new salary
58,842 + 3531.50 = 62,373.50

Replace "increase" with your new information
old salary + (old salary)(percentage) = new salary
58,842 + (58,842)(percentage) = 62,373.50

Now you have the percent in the problem in the problem instead of just the increase. You want to get the percent by itself so subtract 58,842 from both sides and get....

old salary(percentage) = new salary - old salary
58,842(percentage) = 3531.5

Now divide by 58,842 to get the "percentage" by itself

percentage = (new salary - old salary)/old salary
percentage = (3,531.5)/58,842
percentage = .06 or 6%

Answer 4

Calculate (62373.50-58842)/58842*100.
You subtract the old salary from the new salary, and divide the result by the old salary. The result times 100 is the percentage raise.
The reason why you divide by the old salary is that the question is: "what is the percentage raise" which can also be written as "raise as percentage of the old salary".
Suppose you were making $100,000 and now you got a raise to $200,000 (We wish!).
The raise doubled your salary, and we ususally call that a 100% raise [(200000-100000)/100000*100%]
The percentage is always relative to a reference If the question was "how much lower the old salary was in percent relative to the new salary" we would have divided (200000-100000)/200000*100% and gotten 50%. The denominator is always the reference - the number we are measuring relatite to.

Answer 5

Remember, a percentage comes out of a ratio, and a ratio... simply put... is simply a comparative fraction.

Then remember that the fraction is a part of a whole.

In this particular case, setting up the ratio 58,842/62,373.50 allows us to find out what percentage of the teacher's old salary composes the teacher's new salary. The answer to that is about 0.943, or 94.3 percent.

Subtract that from 100 percent, and the answer is a 5.7 percent increase.

Answer 6

From $ 58.842.00 to $ 62,373.50

Just deduct the previous salary from the new salary

62,373.50 - 58,842 = 3531.50

And divide the difference by the previous salary

3531.50/58842 = 0.06

And multiply by 100 to get the percentage

0.06 x 100 = 6 % ===> the answer

Answer 7

you need to find the amount of the raise (62373.50 - 58842 = 3531.50)

and then figure out what percentage that is of the original amount of pay

(3531.5 / 58842 ) x 100 = 6%

Answer 8

OK, you need to solve

58842* (x) = 62373.50

This will give you the total increase. If you subtract 1 from the answer and express the decimal remainder as a percentage you'll have the answer.

Answer 9

First, you need to find the change in pay.

62 373.50-58 842.00= 3531.50.

They want you to find out what percent this increase was in relation to the teacher's original pay.

3531.50=x%(58842.00)
3531.50=588.42x <---decimal place moved since it's a percent

x=3531.50/588.42=6.00%

Answer 10

58842(1+X) = 62373.56

X is the percentage of the raise

58842+58842X = 62373.5

58842X = 62373.5-58842

X = (62373.5 -58842)/58842