SOLUTION: Jon throws all his nickels and dimes in a jar at home each day. He counted all his coins one day and found that he had collected $42.35. If there were five times as many nickels a
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-> SOLUTION: Jon throws all his nickels and dimes in a jar at home each day. He counted all his coins one day and found that he had collected $42.35. If there were five times as many nickels a
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Question 203989: Jon throws all his nickels and dimes in a jar at home each day. He counted all his coins one day and found that he had collected $42.35. If there were five times as many nickels as dimes how many of each coin does he have? Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! let n = number of nickels
let d = number of dimes
since a nickel is worth .05 and a dime is worth .1, then the total money you have is given by the equation:
.05*n + .1*d = 42.35
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since the number of nickels = 6 times the number of dimes, you can replace n with 5d in your equation.
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you get:
.05*5d + .1*d = 42.35
this becomes:
d*(.05*5 + .1) = 42.35 which becomes .35d = 42.35 which becomes d = 121.
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the number of dimes is 121.
the number of nickels is 5 * the number of dimes is 121*5 = 605.
121 * .1 = 12.1
.05 * 605 = 30.25
30.25 + 12.1 = 42.35
your answer is good.
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the key here is the number of nickels and dimes and the value of each.
n = number of nickels and .05 * n = value of the number of nickels
d = number of dimes and .1 * d = value of the number of dimes
.05*n + .1*d = 42.35 is the value equation you have to work with.
you can substitute 5d for n because the number of nickels = 5 times the number of dimes as stated.
this does not change anything else in the value equation except that n has been replaced with 5d because the number of nickels is equal to the number of dimes.
this allows you to reduce the number of unknowns in your equation from 2 to 1 which allows you to solve for the number of dimes which then allows you to solve for the number of nickels.
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You can put this solution on YOUR website! .
Jon throws all his nickels and dimes in a jar at home each day.
He counted all his coins one day and found that he had collected $42.35.
If there were five times as many nickels as dimes how many of each coin does he have?
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This is a typical example of problems on coins
that can be solved MENTALLY in couple of lines without using any equations.
According to the problem, we can group all coins in sets each containing 5 nickels and 1 dime.
Each such a group is worth 5*5 + 10 = 25 + 10 = 35 cents.
Now we can determine the number of such groups of coins. It is
= + = + 1 = + 1 = + 1 = 120 + 1 = 121.
So, there are 121 dimes and 5*121 = 605 nickels. ANSWER
