#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"#
