SOLUTION: bill has 10 coins which are quarters and dimes if his quarters were dimes and his dimes were quarters the total is 30 cents more how many quarters does he has?

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Question 241985: bill has 10 coins which are quarters and dimes if his quarters were dimes and his dimes were quarters the total is 30 cents more how many quarters does he has?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = number of dimes he has
Let q = number of quarters he has
given:
(1)d+%2B+q+=+10
(2) 10d+%2B+25q+%2B+30+=+10q+%2B+25d
---------------------------------------
Notice that on the right side, I make the quarters
worth 10 each and dimes worth 25 each
From (1):
(1) q+=+10+-+d
And, substituting:
(2) 10d+%2B+25%2A%2810+-+d%29+%2B+30+=+10%2A%2810+-+d%29+%2B+25d
10d+%2B+250+-+25d+%2B+30+=+100+-+10d+%2B+25d
-15d+%2B+280+=+15d+%2B+100
30d+=+180
d+=+6
And, since
q+=+10+-+d
q+=+4
He has 4 quarters
check answer:
(2) 10d+%2B+25q+%2B+30+=+10q+%2B+25d
10%2A6+%2B+25%2A4+%2B+30+=+10%2A4+%2B+25%2A6
60+%2B+100+%2B+30+=+40+%2B+150
190+=+190
OK