Final answer:
Zachary needs a minimum of 7 quarters along with his 11 dimes to reach at least $2.75 without exceeding a total of 20 coins.
Step-by-step explanation:
Zachary has 11 dimes, which are worth $0.10 each. This amounts to $1.10 in dimes.
Since Zachary needs to have a minimum of $2.75, we subtract the value of the dimes from this total to find out how much value the quarters need to provide.
$2.75 - $1.10 = $1.65
Each quarter is worth $0.25.
To find out the minimum number of quarters needed to make up $1.65, we divide $1.65 by $0.25.
$1.65 / $0.25 = 6.6
Since Zachary cannot have a fraction of a coin, he needs a minimum of 7 quarters to reach at least $2.75.
With 11 dimes and 7 quarters, Zachary would have 18 coins in total, which is no more than 20 coins.