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2. Mr. Ellis runs an after-school program for nine- and ten-year-olds. Each day the children participate in an
activity or sport and receive a snack. One afternoon, 56 nine-year-olds and 42 ten-year-olds attend the
after-school program.
a. Mr. Ellis wants to divide the group into basketball teams so that each team has the same number of
nine-year-olds, and each team has the same number of ten-year-olds. How many different ways can
he divide the group?
b. What is the greatest number of teams Mr. Ellis can make so each team has the same number of
9-year-olds and the same number of 10-year-olds?
c. Do you think Mr. Ellis should make the greatest number of teams he can? Explain your reasoning.

Respuesta :

frika

Answer:

See explanation

Step-by-step explanation:

Factorize numbers 42 and 56:

[tex]42=2\cdot 3\cdot 7\\ \\56=2\cdot 2\cdot 2\cdot 7[/tex]

These two numbers have common factors 2 and 7. So,

A. Mr. Ellis can divide the group into

  • 1 team = 42 ten-year-olds and 56 nine-year-olds (actually this is not dividing only completing 1 team);
  • 2 teams = 21 ten=year-olds and 28 nine-year-olds in each team;
  • 7 teams = 6 ten-year-olds and 8 nine-year-olds in each team;
  • 14 teams = 3 ten-year-olds and 4 nine-year-olds in each team.

So, there are 3 different ways to divide the group of students into teams.

B. The greatest number of teams Mr. Ellis can make so each team has the same number of 9-year-olds and the same number of 10-year-olds is 14 teams.

C. If Mr. Ellis gives a snack to each winner, then he is interested to give the smallest number of snacks, the smallest number of snacks will be when the number of students in the team is the smallest, the smallest number of students will be when the greatest number of teams are created.

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