# Siri want to buy a book bag. Last week the book bag cost $58 but this week it is on sale for$46. What percent did the price decrease?

Feb 16, 2017

20 20/29% larr" as an exact value"

20.69% " to 2 decimal places" as an approximate value

#### Explanation:

Many an argument has taken place about the proper use of percentages. The symbol % is like a unit of measurement that is worth $\frac{1}{100}$

S0 for example 60% is the same as $60 \times \frac{1}{100} = \frac{60}{100}$

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$\textcolor{b l u e}{\text{Using this to solve the question}}$

Initial state is value $58 This changes to the state of$46

So as a fraction of the initial state the change is $\frac{58 - 46}{58}$

Multiply by 1 and you do not change the vale.

" "color(green)(12/58color(red)(xx1)" "=" "12/58color(red)(xx100/100))

but this is the same as: $\textcolor{g r e e n}{\text{ "=" } \frac{12}{58} \textcolor{red}{\times 100 \times \frac{1}{100}}}$

$\text{ "=" "20color(white)(.) 20/29xx1/100 larr" as an exact value}$

but $\frac{1}{100}$ is the same as % so we have:

$\textcolor{b l u e}{\text{ "=" "20 20/29% larr" as an exact value}}$

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$\textcolor{b r o w n}{\text{What follows is an approximate value}}$

$\textcolor{b l u e}{\text{ "=" "20.69% " to 2 decimal places}}$