SOLUTION: A coin collector has 19 dimes and nickels with a total face value of $1.55. (They are actually worth a lot more.) How many of each coin does she have?
Algebra ->
Customizable Word Problem Solvers
-> Coins
-> SOLUTION: A coin collector has 19 dimes and nickels with a total face value of $1.55. (They are actually worth a lot more.) How many of each coin does she have?
Log On
Question 1162246: A coin collector has 19 dimes and nickels with a total face value of $1.55. (They are actually worth a lot more.) How many of each coin does she have? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52814) (Show Source):
The number of dimes x
The number of nickels (19-x)
The total cents equation is
10x + 5(19-x) = 155 ents, or
2x + (19-x) = 31
2x - x = 31 - 19
x = 12.
ANSWER. 12 dimes and 19-12 = 7 nickels.
CHECK. 12*10 + 7*5 = 155 cents. ! Correct !
You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.
A convenient place to quickly observe these lessons from a "bird flight height" (a top view) is the last lesson in the list.
Read them and become an expert in solution of coin problems.
A student just learning algebra should certainly know how to solve the problem using formal algebra, as shown by the other tutor.
But solving a problem like this informally, with logical reasoning and simple arithmetic, is good mental exercise. It might go something like this:
(1) If all 19 coins were nickels, the total face value would be 95 cents; the actual value is $1.55, or 155 cents. The difference is 60 cents.
(2) Exchanging a nickel for a dime keeps the number of coins the same and increases the face value by 5 cents.
(3) The number of times a nickel needs to be exchanged for a dime, to make up the difference of 60 cents, is 60/5 = 12.
(4) Therefore, the collection contains 12 dimes and 19-12 = 7 nickels.
