Q:

a farmer is putting apples and oranges into boxes to sell at a market. he has 64 apples and 24 oranges. what is the greatest number of boxes he can make using all of the apples and oranges if each box has identical contents?​

Accepted Solution

A:
Answer:8  boxesStep-by-step explanation:To solve this question you must find the prime factors of both numbersApples number:  64 Oranges number: 24Then:64| 232| 2 16| 28 | 24 | 22 | 21  [tex]64=2^6[/tex]24| 212| 26 | 23 | 31[tex]24=2^3 * 3[/tex]Now we take the common factors in both terms with their lowest exponent.2 is a common factor and its smallest exponent is 3: [tex]2^3=8[/tex]So the largest number of boxes you can make is 8The number of apples that each box contains is:[tex]apples = \frac{64}{8}=8[/tex]The number of oranges that each box contains is:[tex]oranges = \frac{24}{8}=3[/tex]