Question

William has 24 cans of fruit and 60 cans of vegetables that he will be putting into bags for a food drive. He wants each bag to have the same number of cans of each type of food. He uses all the cans. Use the drop-down menus to complete the statements below about the number of bags of food William can make. CLEAR CHECK The greatest number of bags William can make is . Each of these bags will have cans of fruit and cans of vegetables. If he made fewer bags, . He could use bags, but this is not the greatest number he could use.

Answer 1

Answer:

See explanation

Step-by-step explanation:

William has 24 cans of fruit and 60 cans of vegetables that he will be putting into bags for a food drive.

Factor number 24 and 60:

$24=2\cdot 12=2\cdot 2\cdot 6=2\cdot 2\cdot 2\cdot 3=2^3\cdot 3\\ \\60=2\cdot 30=2\cdot 2\cdot 15=2\cdot 2\cdot 3\cdot 5=2^2\cdot 3\cdot 5$

Find the greatest common factor

$GCF(24,60)=2^2\cdot 3=12$

Hence, the greatest number of bags William can make is 12.

Each of these bags will have $24\div 12=2$ cans of fruit and $60\div 12=5$ cans of vegetables.

If he made fewer bags, 6 bags, each of these bags will have $24\div 6=4$ cans of fruit and $60\div 6=10$ cans of vegetables.

If he made fewer bags, 4 bags, each of these bags will have $24\div 4=6$ cans of fruit and $60\div 4=15$ cans of vegetables.

If he made fewer bags, 3 bags, each of these bags will have $24\div 3=8$ cans of fruit and $60\div 3=20$ cans of vegetables.

If he made fewer bags, 2 bags, each of these bags will have $24\div 2=12$ cans of fruit and $60\div 2=30$ cans of vegetables.