During a charity run, there are 96 boys and 72 girls participating in a relay race. Each team needs to have the same number of boys and girls.The organizers allowed the greatest possible number of teams to enter the relay race such that every boy and girl was part of a team.How many people will there be on each team?
Question
During a charity run, there are 96 boys and 72 girls participating in a relay race. Each team needs to have the same number of boys and girls.The organizers allowed the greatest possible number of teams to enter the relay race such that every boy and girl was part of a team.How many people will there be on each team?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of boys and girls. The GCD is the largest number that can divide both numbers without leaving a remainder.
Step 1: Find the GCD of 96 (boys) and 72 (girls). The GCD of 96 and 72 is 24.
Step 2: Divide the number of boys and girls by the GCD to find the number of teams. 96 boys ÷ 24 = 4 teams and 72 girls ÷ 24 = 3 teams.
Step 3: Since each team needs to have the same number of boys and girls, the number of teams is limited by the smaller number. So, there are 3 teams.
Step 4: Multiply the number of teams by the number of boys and girls in each team to find the total number of people on each team. 3 teams x 24 people (12 boys and 12 girls) = 72 people.
So, there will be 72 people on each team.
Similar Questions
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 6 boys and 14 girls are competing, how many different ways could the six medals possibly be given out?
A P.E. teacher needs to divide 20 male students and 16 female students into teams, each with the same combination of male students and female students and nobody left out. What is the greatest number of teams that can be formed?
A club has 8 girls and 18 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups the president can make?
A group consists of 4 girls and 7 boys. In how many ways can a group of 5 members be selected if the team has no girls?
At a charity carnival, the ratio of the number of adults to the number of children is 2 : 5. Among the children, the ratio of the number of girls to the number of boys is 3 : 5. A total of 1392 game tickets are given out. Each adult receives 4 tickets and each child receives 10 tickets. How many tickets are given to the boys?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.