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
Algebra.Com
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) (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
-
-----------------------one dime.
------------------twenty-two nickels
Answer by greenestamps(13203) (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
RELATED QUESTIONS
A pile of 40 coins consists of nickels and dimes. The total value of the coins is $3.35.... (answered by checkley77)
a pile of 40 coins consists of nickels and dimes. The total value of the coins is $2.40.... (answered by ikleyn)
a pile of 37 coins consists of nickels and dimes. the total value of the coins is 3.10.... (answered by greenestamps,josgarithmetic)
A pile of coins consists of nickels and dimes.
The total value of coins is $1.20 Find... (answered by sofiyac)
A pile of 40 coins consists of nickels and dimes. The total value of coins is $3.35. Find (answered by checkley77)
A pile of 40 coins consists of nickles and dimes. The total value of coins is $2.40. Find (answered by ewatrrr)
Some coins (dimes and nickels) are in a pile. The total value of the pile is $1.35. The... (answered by josgarithmetic)
a collection of nickels,dimes and quarters consists of 9 coins with a total value of 1.20 (answered by ankor@dixie-net.com)
A collection of nickels, dimes, and quarters consists of 13 coins with a total value of... (answered by josmiceli)