A shelf contains only black, purple and orange pots of paint. The ratio of black pots of paint to purple pots of paint is $14: 9$ . The ratio of purple pots of paint to orange pots of paint is $3: 9$ . $\newline$ Calculate the percentage of pots of paint that are orange. $\newline$ ________ $\%$

Full solution

Q. A shelf contains only black, purple and orange pots of paint. The ratio of black pots of paint to purple pots of paint is

14: 9

. The ratio of purple pots of paint to orange pots of paint is

3: 9

\newline

Calculate the percentage of pots of paint that are orange.

\newline

________

\%

Convert Ratios: Convert the given ratios into a single ratio involving all three colors. The ratio of black to purple is $14:9$ , and the ratio of purple to orange is $3:9$ . To combine these, multiply the parts of the first ratio by the purple part of the second ratio to keep the purple consistent. $\newline$ Calculation: $(14:9) \times (3/3) = 14:9$ and $(3:9) \times (9/3) = 9:27$ . $\newline$ Combined ratio: $14:9:27$ .
Calculate Total Parts: Calculate the total number of parts in the combined ratio. $\newline$ Calculation: $14$ (black) + $9$ (purple) + $27$ (orange) = $50$ parts total.
Determine Orange Percentage: Determine the percentage of orange pots. $\newline$ Calculation: $(27 \text{ orange parts} / 50 \text{ total parts}) \times 100 = 54\%$ .