Even though the number of $1 coin is less, but their total value is till $90 more than the 20c coins.
Take a look at the answer, there are 120 of $1 coins, the value is $120.
There are 150 of 20c coins, value at $30.
So if you remove 30 coins from 20c, to make them the same number as $1 coins, which is 120 coins, the value of the 20c is = $24. Which is a $96 difference.
Basically I am saying, with 30 numbers of 20c coins is only $6. $6 or 30 more 20c coins is not going to be make the value of 20c to be $90 more than total value of $1 coins. Therefore we are correct to assume that the the value of $1 coin is more than value of 20c coins even though there are 30 coins more with 20c. Removing the 20 numbers of 20c coins will only increase the difference further by $6.