For a minute, put aside 8 quarters.
You will have then $4.20 in total, consisting of equal number of nickels and quarters.
You group then these nickels and quarters in sets, containing one nickel and one quarter.
Each group is worth 25+5 = 30 cents, and the number of groups is = 14.
From this point, there is only one step to the final
ANSWER. There are 14 nickels and 14 + 8 = 22 quarters,
CHECK. 14*5 + 22*25 = 620 cents = $6.20. ! Correct !
You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.
A convenient place to quickly observe these lessons from a "bird flight height" (a top view) is the last lesson in the list.
Read them and become an expert in solution of coin problems.