Question 1170525
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A quick informal way to find the solution, without formal algebra, but also without blind trial and error....<br>
(1) Imagine you have 11 coins that are all nickels; the total value would be 55 cents.
(2) The actual total value is 75 cents, which is 20 cents more than that.
(3) Exchange nickels for dimes one at a time, thus keeping the number of coins the same but increasing the total value by 5 cents each time.
Since you need to increase the value by a total of 20 cents, you need to do that exchange 20/5 = 4 times.  So you end up with 4 dimes and 11-4=7 nickels.<br>
ANSWER: 4 dimes and 7 nickels<br>
CHECK: 4(10)+7(5) = 40+35 = 75<br>