Question 0f32b

Jan 5, 2017

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

Explanation:

$\textcolor{b l u e}{\text{Determine the initial relationship}}$

12 of red + 8 of blue = total of 20

So the amount of red as a fraction of the blend quantity is:
$\frac{12}{20} \equiv \frac{12 \div 4}{20 \div 4} = \frac{3}{5}$

$\textcolor{b r o w n}{\text{The volume of paint for the whole job is not really needed as we are after percentage}}$

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$\textcolor{b l u e}{\text{To express this as a percentage}}$

We need to change $\frac{3}{5}$ into $\frac{\text{some value}}{100}$

Known that $5 \times 20 = 100$

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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$\textcolor{b l u e}{\text{To express this as a proportion of 65 pints (not asked for)}}$

$\frac{3}{5} \times 65 \text{ pints" -> 3/(cancel(5)^1)xxcancel(65)^(13)->3xx13=39" pints of red}$