Question

2. Mr. Ellis runs an after-school program for nine- and ten-year-olds. Each day the children participate in an

Answer 1

Answer:

See explanation

Step-by-step explanation:

Factorize numbers 42 and 56:

$42=2\cdot 3\cdot 7\\ \\56=2\cdot 2\cdot 2\cdot 7$

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.