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Joe has a collection of nickels and dimes that is worth $8.30.
If the number of dimes were doubled and the number of nickels were increased by 18,
the value of the coins would be $14.50. How many dimes does he have?
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Let solve it mentally, with easy steps.
We have two collections of coins: one real collection and the other
imaginary collection.
Let construct another imaginary collection, which has the doubled number of dimes,
but the same number of nickels as the real collection.
This another imaginary collection is worth $14.50 - 18*$0.05 = $14.50 - $0.90 = $13.60.
Comparing with the original (real) collection, it has the same number of nickels
and doubled number of dimes.
Hence, the dimes in the original collections are worth the difference between
$13.60 and $8.30, i.e. $5.30, or 530 cents.
From it, you conclude that the number of dimes in the original collection is = 53.
It is your ANSWER.
CHECK. Then the number of nickels in real collection is = = 60
and imaginary collection is worth 2*530 + (60+18)*5 = 1450 cents, or $14.50. ! Correct !
Solved.