Question

Question #0f32b

Answer 1

The amount of red as a percentage of the whole is 60%

Explanation:

`color(blue)("Determine the initial relationship")`

12 of red + 8 of blue = total of 20

So the amount of red as a fraction of the blend quantity is:
`12/20 -=(12-:4)/(20-:4)=3/5`

`color(brown)("The volume of paint for the whole job is not really needed as we are after percentage")`

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`color(blue)("To express this as a percentage")`

We need to change `3/5` into `("some value")/100`

Known that `5xx20=100`

`color(green)([3/5color(red)(xx1)] =[3/5color(red)(xx20/20)]" "=" "60/100)rarr" same as "60%`

So the amount of red as a percentage of the whole is 60%
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`color(blue)("To express this as a proportion of 65 pints (not asked for)")`

`3/5xx65" pints" -> 3/(cancel(5)^1)xxcancel(65)^(13)->3xx13=39" pints of red"`