Percentage Problem

[Bad_at_math]

If someone has a total score at the end of a game of 6,500 points which includes a 30% point bonus, how would you go about finding out what their score was before the 30% bonus was added to it? I mean, I know in this case that the base score was 5,000 and the 30% bonus was 1,500, but how would you go about figuring it out if the only information you were given was that the total was 6,500 and the bonus was 30%? I know that I should probably know how to do this, but I’ve always been extremely bad at math and it’s been many years since I’ve taken any kind of math classes at all.

Thank you in advance for any help.

 

[wjm11]

If someone has a total score at the end of a game of 6,500 points which includes a 30% point bonus, how would you go about finding out what their score was before the 30% bonus was added to it? I mean, I know in this case that the base score was 5,000 and the 30% bonus was 1,500, but how would you go about figuring it out if the only information you were given was that the total was 6,500 and the bonus was 30%?

From the example you gave, you already have all the pieces you need to figure this out. Let’s examine what you did. You took the 5000 and multiplied by .3 (from the 30%), and then you added that amount to the 5000:

(.3)(5000) + 5000 = 1500 + 5000 = 6500

Simple right?

Now suppose you don’t know the base score (5000), so we’ll just call it variable x. Then our equation would have been

(.3)(x) + x = 6500

Now we just simplify and solve for x:

.3x + x = 6500

1.3x = 6500

x = 6500/1.3 = 5000 (base score)

Make sense?

If there had been a 25% bonus instead of 30%, we would have

x = 6500/1.25 = 5200 (base score)

Hope that helps.

 

[Bad_at_math]

Hi, wjm11, thank you very much for your response. Your explanation was very clear and I understand how to solve this kind of problem now.

Thanks again!