Question

There are 84 cans of soda being delivered to a deli, with 36 cans of Pepsi and 48 cans of Sprite. The storeowner wants there to be an equal number of soda cans in each row of the refrigerator. What is the greatest number of rows the storeowner could have? How many cans of Pepsi and how many cans of Sprite are in each row?

Answer 1

The greatest number of rows the storeowner can have is 12, with 3 cans of Pepsi and 4 cans of Sprite per row.

Step-by-step explanation:

The question involves finding the greatest common divisor (GCD) of two numbers to determine the highest number of rows in which an equal number of soda cans can be arranged. The two numbers here are 36 (cans of Pepsi) and 48 (cans of Sprite).

To calculate the GCD, we can use Euclid's algorithm:

1. Divide 48 by 36, which gives a quotient of 1 and a remainder of 12.
2. Divide 36 by 12, which gives a quotient of 3 and a remainder of 0, indicating that 12 is the divisor that goes evenly into both 36 and 48.

Therefore, the greatest number of rows is 12. To find out how many cans of each type would be in each row, divide the number of cans by the number of rows:

• Pepsi: 36 cans ÷ 12 rows = 3 cans per row
• Sprite: 48 cans ÷ 12 rows = 4 cans per row