SOLUTION: Bill has 10 coins, all of which are dimes and quarters. If his dimes were quarters and his quarters were dimes, his coins would total 30 cents more. How many quarters does Bill h

Question 563036: Bill has 10 coins, all of which are dimes and quarters. If his dimes were quarters and his quarters were dimes, his coins would total 30 cents more. How many quarters does Bill have?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Bill has 10 coins, all of which are dimes and quarters. If his dimes were quarters and his quarters were dimes, his coins would total 30 cents more. How many quarters does Bill have?
Let d = the number of dimes
Then 10 - d = the number of quarters
Let the original total = T
Then T = 10d + 25(10-d)
This gives T = 250 - 15d [1]
If the coins are reversed the total is 30 cents more:
T + 30 = 10(10-d) + 25d
This gives T = 70 + 15d [2]
Subtract [2] from [1]:
0 = 180 - 30d
This gives d = 6
So he has 10 - 6 = 4 quarters
Check:
6*10 + 4*25 = 160
4*10 + 6*25 = 190 [30 cents more]

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