Question 1139186
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Using algebra...<br>
q = # of quarters
n = number of nickels<br>
{{{q+n = 12}}}  there are 12 coins total
{{{25q+5n = 220}}}  the total value of the coins is 220 cents<br>
Solve by whatever method you want....
Elimination looks easiest -- multiply the first equation by -5 and add the resulting equation to the second equation, eliminating n; then go from there.<br>
Using logical reasoning and simple mental arithmetic...<br>
(1) If all 12 coins were quarters, the total would be 12*25 = 300 cents; that is (300-220) = 80 cents more than the actual total.
(2) Exchanging one of the quarters for a nickel keeps the total number of coins at 12 and decreases the total value by (25-5) = 20 cents.
(3) You have to do that 80/20 = 4 times to get the total down to the correct 220 cents.<br>
ANSWER: 4 nickels and 8 quarters