Question 1173629
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If a formal algebraic solution is not required, you can get some good mental exercise by solving a problem like this using logical reasoning and some simple arithmetic.<br>
(1) If all 31 coins were nickels, their value would be $1.55, which is $5.20 less than the actual value.
(2) Exchanging a nickel for a quarter keeps the total number of coins the same but increases the value by 20 cents.
(3) The number of times you need to exchange a nickel for a quarter, to make up the addition $5.20 (i.e., 520 cents), is 520/20 = 26.<br>
So the number of quarters is 26, which leaves 5 coins to be nickels.<br>
CHECK: 26(25)+5(5) = 650+25 = 675<br>