SOLUTION: A man has 19 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $ 3.25, how many dimes and how many quarters does he have?

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Question 642011: A man has 19 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $ 3.25, how many dimes and how many quarters does he have?
Found 2 solutions by josmiceli, DrBeeee:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
he has +x+ dimes and +19+-+x+ quarters
given:
+10x+%2B+25%2A%28+19-x+%29++=+325+ ( in cents )
+10x+%2B+475+-+25x+=+325+
+-15x+=+325+-+475+
+-15x+=+-150+
+x+=+10+
+19+-+x+=+19+-+10+
+19+-+x+=+9+
He has 10 dimes and 9 quarters
check:
+10%2A10+%2B+25%2A%28+19-10+%29++=+325+
+100+%2B+25%2A9+=+325+
+100+%2B+225+=+325+
+325+=+325+
OK

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = the number of dimes
Let q = the number of quarters
the total number of coins is the sum of dimes and quarters giving
(1) d + q = 19
Now count up the value of your coins in CENTS. Each dime is ten cents and each quater is 25 cents, the total is $3.25 or 325 CENTS
(2) 10*d + 25*q = 325
Divide out 5 from (2) to simplify to
(3) 2d + 5q = 65
Now solve (1) and (3) simultaneously to yield
(4) d = 10 and q = 9
Right? Yes!
Because (10 + 9) = 19 and 10 dimes is $1 and 9 quarters is $2.25, giving a total of $3.25.