Final answer:
To find the two possible values of z, we look for multiples of 7 between 20 and 30, which are 21 and 28. The difference between these two values is 7.
Step-by-step explanation:
The question asks to determine the two possible values for an unknown positive integer z, where the greatest common factor (GCF) of 35 and z is 7, and z lies between 20 and 30. To find the two possible values of z, we can list the multiples of 7 that fall within the specified range, since 7 will need to be a factor of z to have 7 as its GCF with 35.
21 (3×7)
28 (4×7)
The only multiples of 7 between 20 and 30 are 21 and 28. The difference between these two values is 28 - 21 = 7.