Suppose a certain item increased in price by 18% a total of 5 times and then decreased in price by 10% a total of 2 times. By what overall percent did the price increase?

przesypkai4
2022-07-26
Answered

Suppose a certain item increased in price by 18% a total of 5 times and then decreased in price by 10% a total of 2 times. By what overall percent did the price increase?

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abortargy

Answered 2022-07-27
Author has **19** answers

Step 1

Let, initial price of the item was $x

Now, we have the formulae $A=p(1+p{)}^{t}\to (1)$

$P=\text{Initial price}$

$A=\text{Amount after t times}$

$p=$ Rate of charge

Now, when the price of the item increased by 18% a total of 5 times. Then

$p=\$x,p=0.18,t=5$

From (1) Amount $={A}_{1}=\$x(1+0.18{)}^{5}\phantom{\rule{0ex}{0ex}}=\$(1.18{)}_{x}^{5}$

Step 2

When the price is decreased by 10% a total of 2 times then

$p-\$(1.18{)}^{5}x,p=-0.10(decrease),t=2$

From (1), Amount $={A}_{2}=\$(1.18{)}_{x}^{5}(1-0.10{)}^{2}\phantom{\rule{0ex}{0ex}}=\$(1.18{)}^{5}x(0.9{)}^{2}\phantom{\rule{0ex}{0ex}}=\$1.8531x$

Overall charge in percentage

$=\frac{{A}_{2}-p}{p}\times 100\mathrm{\%}\phantom{\rule{0ex}{0ex}}=\frac{1.8531x}{x}\times 100\mathrm{\%}\phantom{\rule{0ex}{0ex}}=\frac{0.8531x}{x}\times 100\mathrm{\%}\phantom{\rule{0ex}{0ex}}=85.31\mathrm{\%}$

Answer: Overall price increased 85.31%

Let, initial price of the item was $x

Now, we have the formulae $A=p(1+p{)}^{t}\to (1)$

$P=\text{Initial price}$

$A=\text{Amount after t times}$

$p=$ Rate of charge

Now, when the price of the item increased by 18% a total of 5 times. Then

$p=\$x,p=0.18,t=5$

From (1) Amount $={A}_{1}=\$x(1+0.18{)}^{5}\phantom{\rule{0ex}{0ex}}=\$(1.18{)}_{x}^{5}$

Step 2

When the price is decreased by 10% a total of 2 times then

$p-\$(1.18{)}^{5}x,p=-0.10(decrease),t=2$

From (1), Amount $={A}_{2}=\$(1.18{)}_{x}^{5}(1-0.10{)}^{2}\phantom{\rule{0ex}{0ex}}=\$(1.18{)}^{5}x(0.9{)}^{2}\phantom{\rule{0ex}{0ex}}=\$1.8531x$

Overall charge in percentage

$=\frac{{A}_{2}-p}{p}\times 100\mathrm{\%}\phantom{\rule{0ex}{0ex}}=\frac{1.8531x}{x}\times 100\mathrm{\%}\phantom{\rule{0ex}{0ex}}=\frac{0.8531x}{x}\times 100\mathrm{\%}\phantom{\rule{0ex}{0ex}}=85.31\mathrm{\%}$

Answer: Overall price increased 85.31%

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