Percentage problem

[mahdrek]

What number increased by 25% of itself equals 120 ?

I know the answer is 96, and i know 24 comes into play also.....but am having a hard time figuring out the proper equation to get the numbers


25%of 96= 24
24+96=120

percentage=base x rate
percentage=120
but with this problem im not sure the base or the rate, until i looked at back of book for the answers


thank you for any help

 

[Ishuda]

What number increased by 25% of itself equals 120 ?

I know the answer is 96, and i know 24 comes into play also.....but am having a hard time figuring out the proper equation to get the numbers


25%of 96= 24
24+96=120

percentage=base x rate
percentage=120
but with this problem im not sure the base or the rate, until i looked at back of book for the answers


thank you for any help

What Denis said in different words: The base is the "What number" [the n in Denis' post]. Since the starting amount is 100% of the base and it is "increased by 25%" the rate is the sum of the two or 125%. Thus
125% * n = 1.25 * 120
or
n = 120 /1.25 = 96

 

[Probability]

I can't seem to work out how Denis example can find the value of n, I know it will work when I put my figures in it below, but can't solve it.

I don't think this method is a good method but it solves it;

(25) / (125) = 0.2

0.2 x 120 = 24

(125) / (100) = 1.25

(120) / (1.25) = 96

(24 + 96) = 120

 

[Steven G]

What number increased by 25% of itself equals 120 ?

I know the answer is 96, and i know 24 comes into play also.....but am having a hard time figuring out the proper equation to get the numbers


25%of 96= 24
24+96=120

percentage=base x rate
percentage=120
but with this problem im not sure the base or the rate, until i looked at back of book for the answers


thank you for any help

Dennis' method is really the way to go.
I will break it down into smaller steps.
1)You have a number. Call this number n.
2) You want to increase this number by 25% of itself. Increase this number means to add the extra 25% to n. Now since 'of' means to multiply we know that 25% of itself means 25% * n or .25n.
3) you need to add these two numbers (or expressions). We get n + .25n or 1n + .25n which equals 1.25n (just like 3n + 4n = 7n)
4) you are given that this sum equals 120. That is 1.25n = 120
5) To get n we divide both sides by 1.25 and get n= 96.

I hope this helps

 

[mahdrek]

thank you soooo very much...At first Denis' reply seemed very confusing but after Jomo's breakdown I know see Denis' reply as obvious...hopefully I learn something from this