The price of an item changed form $140 to $100. Then later the price increase again from $100 to $140. Which of the two changes was larger in percentage in term and how much percent?
a. 100/140 = 0.714 = 71.4 %.
Change = 71.4 - 100 = -28.6 % = 28.6% decrease.
b. 140/100 = 1.40 = 140%.
Change = 140-100 = 40% increase.
= The largest change.
To determine which change was larger in terms of percentage, we need to calculate the percentage change for each scenario.
Calculating the percentage change involves finding the difference between the new and old values, dividing it by the old value, and then multiplying the result by 100.
Let's calculate the first percentage change when the price changed from $140 to $100:
Percentage change = ((New value - Old value) / Old value) * 100
= ((100 - 140) / 140) * 100
= (-40 / 140) * 100
≈ -0.2857 * 100
≈ -28.57%
The first change represents a decrease of approximately 28.57%.
Now let's calculate the second percentage change when the price increased from $100 to $140:
Percentage change = ((New value - Old value) / Old value) * 100
= ((140 - 100) / 100) * 100
= (40 / 100) * 100
= 0.4 * 100
= 40%
The second change represents an increase of 40%.
Comparing the two changes, we can see that the increase from $100 to $140 represents a larger percentage change (40%) compared to the decrease from $140 to $100 (-28.57%).
Therefore, the second change was larger in percentage terms, with an increase of 40%.