How exactly does the response "infintely many" answer the question of "how many"? I admit that the level of this question is roughly about middle school, but this is what the question asks:

The ratio of nickels to dimes to quarters is 3:8:1. If all the coins were dimes, the amount of money would be the same. Show that there are infinitely many solutions to this problem.


Three nickels and a quarter make up $40$ cents, as do four dimes. As a consequence, the second sentence in your problem does not amount to an additional condition. It follows that any multiple of the package "$3$ nickels, $8$ dimes, and $1$ quarter" solves the problem.
