SOLUTION: A jar of change contains 64 coins consisting only quarters and dimes. The total value of the coins in the jar $13.60. Let q= the number of quarters and d= the number of dimes. Writ

Question 1034811: A jar of change contains 64 coins consisting only quarters and dimes. The total value of the coins in the jar $13.60. Let q= the number of quarters and d= the number of dimes. Writes two equations that describe the information given above. how many of each type of coin is in the jar?

Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A jar of change contains 64 coins consisting only quarters and dimes. The total value of the coins in the jar $13.60. Let q= the number of quarters and d= the number of dimes. Writes two equations that describe the information given above. how many of each type of coin is in the jar?
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q + d = 64
25q + 10d = 1360
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Here's another method:
64 dimes = 640 cents
Each dime replaced by a quarter adds 15 cents.
1360 - 640 = 720
720/15 = 48 quarters replacing dimes
--> 16 dimes
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

Let the number of quarters be q Let the number of dimes be d Value Value Type Number of of of of EACH ALL coin coins coin coins ------------------------------------------- quarters q $0.25 $0.25q dimes d $0.10 $0.10d ------------------------------------------- TOTALS 64 ----- $13.60 The first equation comes from the number of coins column. q + d = 64 The second equation comes from the last column. 0.25q + 0.10d = 13.6 Get rid of decimals by multiplying every term by 100: 25q + 10d = 1360 So we have the system of equations: . We solve by substitution. Solve the first equation for d: q + d = 64 d = 64 - q Substitute (64 - q) for d in 25q + 10d = 1360 25q + 10(64 - q) = 1360 25q + 640 - 10q = 1360 15q + 640 = 1360 15q = 720 q = 48 = the number of quarters. Substitute in d = 64 - q d = 64 - (48) d = 16 dimes. Checking: 48 quarters is $12.00 and 16 dimes is $1.60 That's 64 coins. And indeed $12.00 + $1.60 = $13.60 Edwin

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