Question 1157276
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(1) Using formal algebra....<br>
n nickels
d dimes<br>
n+d=23  [the total number of coins is 23]
5n+10d=120  [the total value of the coins is $1.20 = 120 cents]<br>
Solve the pair of linear equations by your favorite method....<br>
Note the setup using formal algebra is easier if you start with<br>
n nickels
(23-n) dimes  [because the total number of coins is 23]<br>
Then solving the problem involves solving a single equation, instead of a system of two equations:<br>
5(n)+10(23-n) = 120<br>
(2) Using logical reasoning and simple mental arithmetic (if a formal algebraic solution is not required)....<br>
(a) 23 coins all nickels would make the total value 23*5 = 115 cents; that is 5 cents short of the actual total value
(b) Exchange one of the nickels for a dime; that keeps the total number of coins 23 and increases the total value by 5 cents -- giving us the actual total value of 120 cents<br>
ANSWER: 22 nickels and 1 dime<br>