Answer:
The price was increased by 17.15%
Step-by-step explanation:
step 1
we have that
[tex]100\%+3.8\%=103.8\%=103.8/100=1.038[/tex]
Let
x -----> the price of a certain item
we know that
If a price increases by 3.8% a total of 5 times
then
The new price will be equal to multiply the original price by 5 times 1.038
so
[tex]x(1.038)(1.038)(1.038)(1.038)(1.038)=x(1.038)^5[/tex]
step 2
we have that
[tex]100\%-1.4\%=98.6\%=98.6/100=0.986[/tex]
we know that
If a price decreases by 1.4% a total of 2 times
then
The new price will be equal to multiply the actual price by 2 times 0.986
The actual price is [tex]x(1.038)^5[/tex]
so
[tex]x(1.038)^5(0.986)(0.986)=x(1.038)^5(0.986)^2=1.1715x[/tex]
[tex]1.1715-1=0.1715[/tex]
convert to percentage
[tex]0.1715*100=17.15\%[/tex]
therefore
The price was increased by 17.15%
Answer: The price increased by 17.149618%.
Step-by-step explanation:
Given that the price of a certain item increases by 3.8% = 0.038 a total of 5 times.
So every time the price was (1 + 0.038) = 1.038 times the original price.
So after 5 times the price is = [tex]1.038^5=1.205[/tex] times the original price.
Then it decreased by 1.4% twice. So the new price is = [tex]1.205\cdot\left(1-0.014\right)^{2}=1.17149618[/tex] times the original price.
So the percentage increase is = [tex]\left(1.17149618-1\right)\cdot100 \%=17.149618 \%[/tex]
Learn more: https://brainly.com/question/12049968
