SOLUTION: 50 coins in dimes and quarters have a total value of $11.00. How many dimes and quarters are there?

Question 1205731: 50 coins in dimes and quarters have a total value of $11.00. How many dimes and quarters are there?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
50-q of dimes
q quarters

There are still 50 dimes and quarters just as before.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Informally....

If all 50 coins were dimes, the total value would be $5.00.
The actual total value is $11.00, which is $6.00 more.
Since each quarter is worth $0.15 more than each dime, the number of quarters must be $6.00/$0.15 = 600/15 = 40.

ANSWER: 40 quarters and 10 dimes

CHECK: 40($0.25)+10($0.10) = $10.00+$1.00 = $11.00

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And here is a really unorthodox solution, treating the problem as a mixture problem.

You are mixing quarters worth 25 cents each with dimes worth 10 cents each to get a mixture of coins worth an average of $11.00/50 = 22 cents each.
Since 22 cents is 4/5 of the way from 10 cents to 25 cents, 4/5 of the coins must be quarters. (From 10 to 25 is a difference of 15; from 10 to 22 is a difference of 12; 12/15 = 4/5.)
4/5 of 50 is 40.

ANSWER (again, of course): 40 quarters and 10 dimes

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