Question

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?

Answer 1

`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 `1/100`

S0 for example 60% is the same as `60xx1/100=60/100`

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`color(blue)("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 `(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: `color(green)(" "=" "12/58color(red)(xx100 xx 1/100))`

`" "=" "20color(white)(.) 20/29xx1/100 larr" as an exact value"`

but `1/100` is the same as % so we have:

`color(blue)(" "=" "20 20/29% larr" as an exact value")`

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`color(brown)("What follows is an approximate value")`

`color(blue)(" "=" "20.69% " to 2 decimal places")`