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

See explanation

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/ 12=2` cans of fruit and
`60/ 12=5` cans of vegetables.

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

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

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

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