SOLUTION: P has pennies, dimes, and quarters. They add up to a total of $5.59. There are 43 coins and the number of quarters plus 9 equals the number of pennies and dimes. How many quarters?

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Question 657388: P has pennies, dimes, and quarters. They add up to a total of $5.59. There are 43 coins and the number of quarters plus 9 equals the number of pennies and dimes. How many quarters? pennies? and dimes does P have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+p+ = number of pennies
+d+ = number of dimes
+q+ = number of quarters
given:
(1) +p+%2B+d+%2B+q+=+43+
(2) +p+%2B+10d+%2B+25q+=+559+ ( in cents )
(3) +q+%2B+9+=+p+%2B+d+
-------------------
Substitute (3) into (1)
(1) +q+%2B+9+%2B+q+=+43+
(1) +2q+=+34+
(1) +q+=+17+
-------------
(3) +17+%2B+9+=+p+%2B+d+
(3) +p+=+26+-+d+
Substitute this back into (2)
-----------------
(2) +26+-+d+%2B+10d+%2B+25%2A17+=+559+
(2) +26+%2B+9d+%2B+425+=+559+
(2) +9d+=+559+-+425+-+26+
(2) +9d+=+108+
(2) +d+=+12+
--------------
(1) +p+%2B+d+%2B+q+=+43+
(1) +p+%2B+12+%2B+17+=+43+
(1) +p+=+43+-+12+-+17+
(1) +p+=+14+
-------------
P has 14 pennies
12 dimes
17 quarters
-----------
check:
(2) +p+%2B+10d+%2B+25q+=+559+
(2) +14+%2B+10%2A12+%2B+25%2A17+=+559+
(2) +14+%2B+120+%2B+425+=+559+
(2) +559+=+559+
OK