Lola is placing appetizers on plates. she has 63 spring rolls and 84 cheese cubes. she wants to include both appetizers on each plate. Each plate must have the SAME numbers of spring rolls and cheese cubes. what is the greatest number of plates she can make using ALL of the appetizers? how many of each type of appetizer will be on each of the plates?
Lola is placing appetizers on plates. She has 63 spring rolls and 84 cheese cubes. She wants to include both appetizers on each plates. Each plate must have the same numbers of spring rolls and cheese cubes. What is the greatest number of plates she can make using all of the appetizers? How many of each type of appetizer will be on each of these plates?
To find out the greatest number of plates Lola can make, we need to determine the common factor between 63 and 84, which represents the same number of spring rolls and cheese cubes on each plate.
We can begin by finding the prime factors of both 63 and 84:
Prime factors of 63: 3 × 3 × 7
Prime factors of 84: 2 × 2 × 3 × 7
To find the common factors, we need to take the minimum exponent for each prime factor:
Common factors: 3 × 7
Therefore, Lola can make a maximum of 3 × 7 = 21 plates using all the appetizers.
To determine the number of each type of appetizer on each plate, we divide the total quantity of each appetizer by the number of plates:
Number of spring rolls per plate = 63 ÷ 21 = 3 spring rolls
Number of cheese cubes per plate = 84 ÷ 21 = 4 cheese cubes
Hence, Lola can make a maximum of 21 plates, and each plate will have 3 spring rolls and 4 cheese cubes.
What is the greatest factor of these two numbers?
63:
3, 21
7, 9
84:
2, 42
3, 28
4, 21
6, 14
7, 12