SOLUTION: Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does L
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Question 1145667: Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have?
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
Using formal algebra....
d = # of dimes
q = # of quarters
(1) 10d+25q = 620 [the value of the dimes (10 cents each) and quarters (25 cents each) is $6.20 = 620 cents]
(2) d = 3q+18 [the number of dimes is 18 more than 3 times the number of quarters]
Solve the pair of equations. Probably the easiest method is to substitute (2) into (1) and solve for q; then use that value of q in either equation to solve for d.
I leave it to you to get the practice finishing solving the problem using formal algebra.
Using logical reasoning and simple mental arithmetic....
(1) Count the 18 "extra" dimes. Their value is 180 cents; that leaves 440 cents for the remaining coins.
(2) The remaining coins are 3 dimes for each quarter. Imagine the remaining coins in groups each consisting of 1 quarter and 3 dimes. The value of 1 quarter and 3 dimes is 55 cents.
(3) The number of groups at 55 cents each required to make the remaining 440 cents is 440/55 = 8. In those 8 groups there are 8 quarters and 8*3=24 dimes.
(4) So all together there are 8 quarters and 24+18=42 dimes.
(3) The number of groups of
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