Percent Difference

[NeuroticMathMom]

484.03/1.07 = 452.36
452.36*1.05=474.98

Contrast
484.03*.07= 33.88
484.03-33.88=450.15
450.15*1.05=472.66

I cant figure out why the amounts are different if they are basically doing the same thing.

 

[HallsofIvy]

No, you are NOT "doing the same thing". In the first, where you divide 484.03 by 1.07, you are finding x such that 484.02= (1.07)x. That is, you are finding x such that 484.03 is 7% of x larger than x.

In the second, where 484.03 is multiplied by .07, then that is subtracted from 484.03, you are finding x such that x is 7% less than 484.03- that is 7% of 484.03. You are subtracting 7% of different numbers.

 

[Ishuda]

484.03/1.07 = 452.36
452.36*1.05=474.98

Contrast
484.03*.07= 33.88
484.03-33.88=450.15
450.15*1.05=472.66

I cant figure out why the amounts are different if they are basically doing the same thing.

In the first case you have 452.36 is 107% of 484.03 and 474.98 is 105% of 452.36

In the second case you have 450.15 is 93% of 484.03 and 472.66 is 105% of 450.15

If you change the numbers or percentages, shouldn't you expect different results?

Surely you didn't expect that if a is (1-x)%, i.e. 0.97%, of b, that b would be (1+x) percent of a, i.e. 1.03 percent. That sounds like something I would do EDIT: Of course it is approximately true if x is (very)close to zero. After all 5 is halfway to infinity.