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

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?
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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