Multiple choice

A tin of paint of a particular shade of colour is a mixture of red, blue and yellow. $\displaystyle \frac{1}{4}$ of the total volume of paint is made up of red paint and the ratio of the volume of red paint to that of blue paint is 3 : 2. Find the total volume of paint that will contain 84 mL of yellow paint.

  1. $120$ mL
  2. $140$ mL
  3. $144$ mL
  4. $168$ mL
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Red = 1/4 total. Ratio Red:Blue = 3:2, so Blue = (2/3) * Red = (2/3) * (1/4) = 1/6 total. Yellow = 1 - (1/4 + 1/6) = 1 - 5/12 = 7/12 total. 7/12 * Total = 84, so Total = 144 mL.

AI explanation

Red paint makes up one quarter of the total volume, and since the ratio of red to blue is 3 to 2, blue paint makes up one sixth of the total volume. Together, red and blue account for five twelfths of the volume, leaving seven twelfths of the total volume for yellow paint. Set up the equation where seven twelfths of the total volume equals 84 mL, and solving this gives a total volume of 144 mL.

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