Joe has a collection of nickels & dimes that is worth $8.55 If the number of dimes was tripled & the number of nickels was decreased by 2, the value of the coins would be $10.45 How many nickels and dimes does he have?

If Joe adds 2 nickels to his second amount, he will have 3 times the dimes he has in the first amount. That is, the two amounts will now differ by twice the number of dimes Joe has.   ($10.45 + 2*.05) - $8.55 = 2*dimes   $2.00 = 2*dimes   $1.00 = dimes   ($8.55 - $1.00)/$.05 = 151 Joe has 10 dimes and 151 nickels.

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Check   $3.00 + 149*$.05 = $3.00 + $7.45 = $10.45