Final answer:
Joey calculated the sum of the largest and smallest two-digit numbers that are multiples of three. Zoey calculated the sum of the largest and smallest two-digit numbers that are not multiples of three. The difference between their answers is 2.
Step-by-step explanation:
To find the largest and smallest two-digit numbers that are multiples of three, we need to look at the multiples of three between 10 and 99. The multiples of three in this range are 12, 15, 18, ..., 96, 99. The largest two-digit number is 99, and the smallest two-digit number is 12. So, Joey's sum is 99 + 12 = 111.
To find the largest and smallest two-digit numbers that are not multiples of three, we need to look at the numbers between 10 and 99 that are not divisible by three. The numbers not divisible by three are 10, 11, 13, ..., 98. The largest two-digit number not divisible by three is 98, and the smallest two-digit number not divisible by three is 11. So, Zoey's sum is 98 + 11 = 109.
The difference between Joey's sum and Zoey's sum is 111 - 109 = 2.