Understanding Percentage Growth in Price Changes

[xeon123]

I'm trying to understand this problem.

If a lollipop costed $6 and now it costs $8, how much percent the price grow?

I think the answer is ((8-6)/8)*100=25%

So I'm trying to apply this solution to the new problem. If a lollipop costed $1, and now it costs $2, how much percent the price grow?
((2-1)/2)*100=50%, but it should be 100%.

Can anyone help me with this problems?

 

[Ray Vickson]

I think you already know the answer: what must be in the denominator in order that your second example gives you 100%?

RGV

 

[xeon123]

In the denominator should be 1. But in the first equation it should be 8. This is the part that I don't get it. I'm putting in the denominator the current price.

 

[Ray Vickson]

I understand what you are doing. I don't understand *why* you are doing it differently in the two examples.

RGV

 

[Mark44]

The denominator should have the price we're calculating the percent increase/decrease for.

For your two examples, the starting prices were $6 and $1, respectively, so those are the numbers you need to use in the denominator.

On the other hand, if the price of something goes down from from $10 to $8, then the percent decrease is (10 - 8)/10 * 100 = 20 %.

If the price happened to go back up by $2, then the percent increase would be (10 - 8)/8 * 100 = 25%. The reason we're getting a different number is we're using a different base or starting point.

 

[xeon123]

I wasn't understanding the problem because I got different percentage values. In the example of Mark44 the same price decreased 20% to pass from $10 to $8, and the increased 25% to pass from $8 to $10. Projecting my question with Mark 44 explanation, my confusion was in the different percentage values. I was thinking why a price decreases 20%, and it has to increase 25%, and not 20%, to get to the initial value? Now, I understand.

 

[e^(i Pi)+1=0]

$\frac{new-old}{old}$(100)

I wasn't understanding the problem because I got different percentage values. In the example of Mark44 the same price decreased 20% to pass from $10 to $8, and the increased 25% to pass from $8 to $10. Projecting my question with Mark 44 explanation, my confusion was in the different percentage values. I was thinking why a price decreases 20%, and it has to increase 25%, and not 20%, to get to the initial value?

Because the amount you're multiplying the percent by is smaller.

 

[HallsofIvy]

In the denominator should be 1. But in the first equation it should be 8. This is the part that I don't get it. I'm putting in the denominator the current price.

That's because the answer you gave to the first problem is wrong. If the lollypop increased from 6$ to 8$ then it increased by $2 and that is 2/6= 1/3 of the original price. The price of the lollypop increased by 1/3 or 33 and 1/3 percent, NOT 25%.