color(blue)("Determine the initial relationship")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)=3/51220≡12÷420÷4=35
color(brown)("The volume of paint for the whole job is not really needed as we are after percentage")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")To express this as a percentage
We need to change 3/535 into ("some value")/100some value100
Known that 5xx20=1005×20=100
color(green)([3/5color(red)(xx1)] =[3/5color(red)(xx20/20)]" "=" "60/100)rarr" same as "60%[35×1]=[35×2020] = 60100→ 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)")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"
