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): You can put this solution on YOUR website!
d for dimes
q for quarters


Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.

Solved.

For coin problems, see the lessons
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
in this site.


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