Solve for X: x-12.43%=34.54

[GoldenEnigma]

I recently ran into this problem and it has me completely stumped.

x - (any percentage up to two decimal places) = (any number up to two decimal places)

Some examples:

x-74.24%=12.65

x-2.54%=202.41

x-22.75%=229.48

How would you solve for x using a calculator? I searched all over on the internet for help, but nothing seems to give me the correct answer.

 

[Otis]

Solve for X: x-12.43%=34.54 …

Hello. First, a note about notation. In math, symbols x and X are different, so we don't use them interchangeably. Also, when we state a percent, we always need to indicate the whole. That is, you need to specify that you're talking about 12.43% of x. You may already know that % means 'per hundred'. In other words:

12.43% = 12.43÷100 = 0.1243

We call 0.1243 the 'decimal form' of 12.43%, and I've used the decimal form below.

x - 0.1243x = 34.54

Factor out x

x(1 - 0.1243) = 34.54

Divide both sides by (1 - 0.1243)

x = 34.54 / (1 - 0.1243)

Using a basic calculator, you can evaluate that expression for x in two steps (do what's inside the parentheses first):

1 - 0.1243 = 0.8757

34.54 / 0.8757 = 39.44273153

Round the answer, as desired.

x = 39.44

?

 

[GoldenEnigma]

Thanks for your quick reply I understand it now

 

[HallsofIvy]

What you have written makes no sense! The problem, I suspect, is that you don't understand what a "percent" really is. In particular, you cannot subtract a percent, like "72.24%", from a number, like "x". A percent always has to be given as a percent of some number. In the first equation you are subtracting 72.24% of what number. I suspect the problem specified "72.24% of x".

I feel sure the equations you have written here were not given in your textbook. (If they were you need a new textbook! My guess is that the first exercise was something like "x minus 72.27 of itself" or perhaps "x is discounted by 72.24%". Could you give the problem exactly as it is in your text book?

Also "72.24%" of a number is 0.7224 times that number ("per cent" means "per hundred" so the number is divided by 100). "x minus 72.24% of x", or however it is phrased, is x- 0.7224x= (1- 0.7224)x= 0.2776x so the first equation is 0.2776x= 12.65. Can you solve that?

 

[Dr.Peterson]

Presumably what these mean is "x reduced by 74.24%", that is, "x - 74.24% of x". You should never write that as"x - 74.24%", which is misleading.

Some calculators (for business applications?) have % keys that handle percent increase and decrease problems using a notation like x - 74.24%, but you would have to read the manual to be sure how it works, especially if you want to "undo" a percent increase, as in your problems. I avoid percent keys, both because calculators are inconsistent so I can't be sure what will happen, and because the notation they use is bad mathematically, leading to confusion for algebra students.

To solve it yourself, write the equation x - 0.7424x = 12.65 and solve for x, as Otis explained well.