Question

Для спортивной команды купили 45 маек и 27 футболок. Какое наибольшее число спортсменов может быть в команде, если каждый получит одинаковый набор одежды и будут использованы все вещи.

Answer 1

9 человек, тогда в данном случае каждый спортсмен получит по 3 футболки и по 5 маек

Answer 2

Problem Analysis

To determine the maximum number of athletes that can be in the team, given the purchase of 45 jerseys and 27 t-shirts, we need to find the greatest common divisor (GCD) of these two numbers. The GCD represents the largest number that can evenly divide both 45 and 27, which will give us the maximum number of athletes that can be in the team with an equal distribution of clothing.

Solution

To find the GCD of 45 and 27, we can use the Euclidean algorithm. The algorithm works by repeatedly subtracting the smaller number from the larger number until the two numbers become equal. The resulting number is the GCD.

Let's calculate the GCD of 45 and 27:

1. Subtract 27 from 45: 45 - 27 = 18 2. Subtract 18 from 27: 27 - 18 = 9 3. Subtract 9 from 18: 18 - 9 = 9 4. Subtract 9 from 9: 9 - 9 = 0

Since the result is 0, we have found the GCD of 45 and 27, which is 9.

Answer

The maximum number of athletes that can be in the team is 9. Each athlete will receive an equal set of clothing, consisting of 5 jerseys and 3 t-shirts.

Explanation

By finding the GCD of 45 and 27, we determined the largest number that can evenly divide both quantities. In this case, the GCD is 9, which means that we can form 9 groups of athletes, with each group receiving 5 jerseys and 3 t-shirts. This ensures that all clothing items are used and each athlete receives an equal set of clothing.