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?

1 Answer
Feb 16, 2017

Answer:

#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#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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")#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("What follows is an approximate value")#

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