Question 1124531
<br>
The problem can be solved informally using logical reasoning:<br>
(1) Take one quarter -- value $0.25.
(2) Since the number of dimes is twice the number of quarters, now take two dimes -- value $0.20.  The total value of the coins is now $0.25+$0.20 = $0.45.
(3) Since the number of nickels is three times the number of dimes, now take 6 nickels -- value $0.30.  The total value of the coins is now $0.45+$0.30 = $0.75.<br>
The total Marilyn has is $2.25, which is 3 times $0.75.  So what Marilyn has is three groups of coins, each containing 1 quarter, 2 dimes, and 6 nickels.<br>
So what Marilyn has is 3 quarters, 6 dimes, and 18 nickels.<br>
Solving the problem with formal algebra takes virtually the same path:<br>
let x = number of quarters
then 2x = number of dimes
then 6x = number of nickels<br>
x(.25)+2x(.10)+6x(.05) = 2.25
.25x + .20x + .30x = 2.25
.75x = 2.25
x = 2.25/.75 = 3<br>
quarters: x = 3
dimes: 2x = 6
nickels: 6x = 18<br>
You should, of course, understand the formal algebraic solution; for more complicated problems, the formal algebra will often be easier to use than informal logical reasoning.<br>
But thinking through problems like this using logical analysis is good brain exercise.