Try using equations to solve the problem.
Let Q be the number of quarters Thomas spent.
Let N be the number of nickels and D be the number of dimes.
Then "he would have needed 20 more dimes than quarters" is the same as writing:
Q + 20 = D
and "one more than twice as many nickels as quarters" means:
2Q + 1 = N
The question asks for the cost (let's call that C). So you also know that if he paid in quarters,
(.25)Q = C
and if he paid in the nickels and dimes,
(.10)D + (.05)N = C
Logically, if two different things equal a common third thing, they equal each other, so
.25Q = .10D + .05N
Now you can use the two earlier equations to substitute for D and N and then solve for Q. That will determine the cost of the item.
Hope this helps,
Stephen La Rocque.