Final answer:
The largest even number group for both 104 nickels and 88 dimes is 22 after determining the highest even divisor that they can both be divided by, considering the limiting factor of the smaller number of coins.
Step-by-step explanation:
To find the number of even-numbered groups that can be made with 104 nickels and 88 dimes, we first determine the largest even number that both quantities can be divided by. The highest even divisor for 104 nickels is 104 itself, since it's an even number and can be divided into one group of 104 nickels. For the 88 dimes, the highest even divisor is also 88 itself, allowing for one group of 88 dimes.
However, if the question requires the number of groups to be the same for both coins, the limiting factor would be the smaller number of dimes. In that case, we would look for the highest even divisor of 88 that 104 can also be divided by. This would be 8 since 104 divided by 8 gives us 13, which is an odd number, so we need to divide by another even number, 4. So the number of groups is the 104 nickels divided by 4, which gives us 26 groups of nickels, and 88 dimes divided by 4, which also gives us 22 groups of dimes, for a total of 22 even-numbered groups.