SOLUTION: In a collection of dimes and quarters, the number of dimes is eight less than twice the number of quarters. The value of the collection is $8.20. Find the number of dimes and quart
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Question 1042758: In a collection of dimes and quarters, the number of dimes is eight less than twice the number of quarters. The value of the collection is $8.20. Find the number of dimes and quarters. Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39620) (Show Source):
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In a collection of dimes and quarters, the number of dimes is eight less than twice the number of quarters.
The value of the collection is $8.20. Find the number of dimes and quarters.
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Let me solve it mentally, without using equations.
Add 8 dimes to the collection (mentally).
Then the total would be $ 8.20 + $0.80 = $9.00.
Then $9.00 consists of some number of dimes (d) and twice the number of quarters.
So, we have 3d coins, which we can re-group into d groups consisting of two quarters and one dime each.
d groups of coins worth 2*50+10 = 60 cents each group.
Obviously, the number of groups is = 15.
Hence, originally we had 2*15 = 30 quarters and 15-8 = 7 dimes.
Check. 30*25 + 70 = 750 + 70 = 820 cents.
Answer. 30 quarters and 7 dimes.
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