Question

Rita decides to decorate her wall with three colors red, blue and orange. She wants to use blue color for $ \dfrac{2}{5} $ part of the wall, red color for $ \dfrac{2}{3} $ of the remaining part and orange for the rest.
A) What fraction of the wall will be colored red?
B) What fraction of the wall will be colored orange?
C) If the wall has an area of $ 25 $ square meters, what area of the wall will be orange colored?

Answer 1

Hint: In this question, it has been given that Rita decides to decorate her wall with three colors and the fraction of what she wants to use is also given. Here first we will consider the C) and find the area of each color she wants to use and finally, find the fraction of the wall that will be colored by each.

Complete step-by-step answer:
C) Let us consider, total area of the wall = $ 25\;{m^2} $
Now, area of wall will be colored blue color = $ \dfrac{2}{5} \times 25 = 10\;{m^2} $
Therefore, area of wall will be left = $ \left( {25 - 10} \right)\;{m^2} $ $ = 15\;{m^2} $
Area of the wall will be colored red color = $ \dfrac{2}{3} \times 15 = 10\;{m^2} $
Now, the area of the wall will be left = $ 15 - 10 = 5\;{m^2} $
Hence, the area of the wall will be colored red is $ 10\;{m^2} $ .
Area of the wall will be colored blue is $ 10\;{m^2} $ .
Area of the wall will be colored orange is $ 5\;{m^2} $ .
A) Fraction of the wall will be colored blue= $ \dfrac{{10}}{{25}} $ = $ \dfrac{2}{5} $
B) Fraction of the wall will be colored red= $ \dfrac{{10}}{{15}} $ = $ \dfrac{2}{3} $

Note: In this question, it is important to note here that we need to determine the area of each color, to determine the fraction of each color as the faction that Rita wants to use is given. If the faction of color is not given in the question then we can conclude directly that the faction of each color is $ \dfrac{1}{3} $ as there are three colors.