Question

The market bought grapes for $0.87 a pound and sold them for $1.09 a pound. What is the percent of increase rounded to the nearest tenth?

Answer 1

Unless told otherwise the increase will be compared to the original value. So we are comparing to $0.87

Increase is the change which is `$1.09-$0.87 = $0.22`

So expressed as a fraction the change is `($0.22)/($0.87)`

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`color(blue)("Using the shortcut method")`

The percentage change is: `(0.22-:0.87)xx100= 25.28735...%`

Rounded to the nearest tenth `25.3%` to 1 decimal place

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`color(blue)("Using first principle method")`

A percentage in fraction form is `("some number")/100`

So we need to change `($0.22)/($0.87)` such that the bottom number (denominator) is 100.

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So we need to manipulate $0.87 this way:
`0.87xx100/0.87` is the same as `" "0.87/0.87xx100" " =" 2 1xx100`

To maintain the correct ratio what we do to the bottom we also do to the top.
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Multiply top and bottom by `100/0.87` giving:

`(0.22xx100/0.87)/(0.87xx100/0.87) larr"the top is the same as the shortcut"`

giving

`" "(25.28735...)/100` which is the same as 25.3% to 1 decimal place.
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`color(purple)("Footnote")`

`color(purple)("Did you know that "%" is really a unit of measurement")`

In the same way that centimetre is the unit size of `" "(1" metre")/100`

`%` is the unit size of `1/100` of something.

So for example `60% -> 60/100` of something