FMU 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 lesa. blonde haired students than brown haired students and the number of red haired students was one third of those with blonde hair.

Let's define the number of students in each hair color group: - Let \( b \) be the number of brown-haired students. - Let \( k \) be the number of black-haired students. - Let \( l \) be the number of blonde-haired students. - Let \( r \) be the number of red-haired students. From the problem, we have the following relationships: 1. There are three times as many brown-haired students as black-haired students: \[ b = 3k \] 2. There are six less blonde-haired students than brown-haired students: \[ l = b - 6 \] 3. The number of red-haired students is one third of those with blonde hair: \[ r = \frac{1}{3}l \] 4. The total number of students is 24: \[ b + k + l + r = 24 \] Now, we can substitute the expressions for \( b \), \( l \), and \( r \) into the total equation. Substituting \( b = 3k \) into the equation for \( l \): \[ l = 3k - 6 \] Substituting \( l \) into the equation for \( r \): \[ r = \frac{1}{3}(3k - 6) = k - 2 \] Now we can substitute \( b \), \( l \), and \( r \) into the total number of students equation: \[ 3k + k + (3k - 6) + (k - 2) = 24 \] Combining like terms: \[ 3k + k + 3k - 6 + k - 2 = 24 \] \[ 8k - 8 = 24 \] Adding 8 to both sides: \[ 8k = 32 \] Dividing by 8: \[ k = 4 \] Now we can find the number of students in each group: - \( b = 3k = 3 \times 4 = 12 \) - \( l = b - 6 = 12 - 6 = 6 \) - \( r = k - 2 = 4 - 2 = 2 \) Now we can summarize the number of students in each hair color group: - Brown-haired students: \( b = 12 \) - Black-haired students: \( k = 4 \) - Blonde-haired students: \( l = 6 \) - Red-haired students: \( r = 2 \) Finally, let's verify the total: \[ b + k + l + r = 12 + 4 + 6 + 2 = 24 \] The numbers add up correctly. Therefore, the distribution of students is: - Brown: 12 - Black: 4 - Blonde: 6 - Red: 2