Number 3
4 marks · HardA school is holding a sports day with relay races. There are 198 boys and 135 girls. Each relay team must have the same number of boys and the same number of girls, and no students can be left out.
Find the greatest number of teams that can be formed and state how many boys and how many girls would be in each team.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
The greatest number of teams is 9, with 22 boys and 15 girls in each team.
Also accept: The highest common factor is 9. Each team has 22 boys and 15 girls.
Common mistakes: Incorrect HCF calculation; swapping boys and girls.
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Express 198 and 135 as products of their prime factors.
M2 · 1 mark · Find the HCF of 198 and 135.
A1 · 1 mark · Obtain correct HCF = 9 and state as the number of teams.
A2 · 1 mark · State correct number of boys (22) and girls (15) per team. (follow-through)
Worked solution
Prime factors: 198 = 2 × 3^2 × 11; 135 = 3^3 × 5.
HCF is 3^2 = 9.
So, there will be 9 teams.
Number of boys per team: 198 / 9 = 22. Number of girls per team: 135 / 9 = 15.
Final answer: 9 teams, with 22 boys and 15 girls in each team.