Question 5 Miss Jones decided to divide her class of 24 students into groups according to the colour of their hair: brown, black, blonde and red. She counted three times as many brown haired students as those with black hair. There were six less blonde haired students than brown haired students and the number of red haired students was one third of those with blonde hair. How many students of each hair colour did Miss Jones have in her class?

Let's denote the number of students with black hair as \( x \). According to the given information: - The number of brown-haired students is three times the number of black-haired students, so the number of brown-haired students is \( 3x \). - The number of blonde-haired students is six less than the number of brown-haired students, so the number of blonde-haired students is \( 3x - 6 \). - The number of red-haired students is one-third of the number of blonde-haired students, so the number of red-haired students is \( \frac{1}{3} \times (3x - 6) \). The total number of students in the class is 24, so we can set up the equation: \[ x + 3x + (3x - 6) + \frac{1}{3} \times (3x - 6) = 24 \] Now, we can solve this equation to find the number of students with each hair color. Solve the equation by following steps: - step0: Solve for \(x\): \(x+3x+\left(3x-6\right)+\frac{1}{3}\left(3x-6\right)=24\) - step1: Simplify: \(8x-8=24\) - step2: Move the constant to the right side: \(8x=24+8\) - step3: Add the numbers: \(8x=32\) - step4: Divide both sides: \(\frac{8x}{8}=\frac{32}{8}\) - step5: Divide the numbers: \(x=4\) The solution to the equation is \( x = 4 \). Now, we can calculate the number of students with each hair color: - Black-haired students: \( x = 4 \) - Brown-haired students: \( 3x = 3 \times 4 = 12 \) - Blonde-haired students: \( 3x - 6 = 3 \times 4 - 6 = 6 \) - Red-haired students: \( \frac{1}{3} \times (3x - 6) = \frac{1}{3} \times (3 \times 4 - 6) = 2 \) So, Miss Jones had 4 black-haired students, 12 brown-haired students, 6 blonde-haired students, and 2 red-haired students in her class.