SOLUTION: Solve the following using a system of equations: Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters and how many dimes does

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Solve the following using a system of equations: Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters and how many dimes does       Log On

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Question 418862: Solve the following using a system of equations:
Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters and how many dimes does she have?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = number of dimes
Let q = number of quarters
given:
(1) d+%2B+q+=+100+
(2) 10d+%2B+25q+=+1405+
Multiply (1) by 10 and
subtract (1) from (2)
(2) 10d+%2B+25q+=+1405+ (in cents)
(1) -10d+-+10q+=+-1000+
+15q+=+405+
q+=+27+
and
d+=+100+-+q+
d+=+100+-+27+
d+=+73+
The number of dimes is 73
The number of quarters is 27
check:
(2) 10d+%2B+25q+=+1405+
(2) 10%2A73+%2B+25%2A27+=+1405+
730+%2B+675+=+1405+
+1405+=+1405+
OK