SOLUTION: A pile of 23 coins consists of nickels and dimes. The total value of the coins is $1.20. Find the number of each type of coin

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Question 1157276: A pile of 23 coins consists of nickels and dimes. The total value of the coins is $1.20. Find the number of each type of coin
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
This is like a two-part mixture problem.
d, how many dimes
23-d, how many nickels

10d%2B5%2823-d%29=120
-
2d%2B%2823-d%29=24
2d-d=24-23
highlight%28d=1%29-----------------------one dime.
highlight%2822%29nickels------------------twenty-two nickels

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Using formal algebra....

n nickels
d dimes

n+d=23 [the total number of coins is 23]
5n+10d=120 [the total value of the coins is $1.20 = 120 cents]

Solve the pair of linear equations by your favorite method....

Note the setup using formal algebra is easier if you start with

n nickels
(23-n) dimes [because the total number of coins is 23]

Then solving the problem involves solving a single equation, instead of a system of two equations:

5(n)+10(23-n) = 120

(2) Using logical reasoning and simple mental arithmetic (if a formal algebraic solution is not required)....

(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

ANSWER: 22 nickels and 1 dime