Question 1032769: sarah has some dimes and quarters. If she has 29 coins worth a total of $4.40, how many of each type of coin does she have? Found 2 solutions by Alan3354, FrankM:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! sarah has some dimes and quarters. If she has 29 coins worth a total of $4.40, how many of each type of coin does she have?
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d + q = 29 (# of coins)
10d + 25q = 440 (value of coins)
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d = 29 - q
Sub for d
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10(29-q) + 25q = 440
290 + 15q = 440
15q = 150
q = 10 quarters
d = 19 dimes
You can put this solution on YOUR website! Let me offer the single variable method, which I think is the simplest to understand and use.
(Note - as I published, I saw Alan solved using 2 variables. You see we got the same answer. Use the method you find most comfortable to use. We proved there's often more than one way to approach a problem.)
Sarah has X dimes, they are worth 10X cents
She has (29-X) quarters, they are worth 25(29-X) cents
Her total value, is 440 cents, so
10X+25(29-X) = 440
10X + 725 - 25X = 440
-15X = -285
X = 19 (dimes) and 29-X=10 (quarters)
19 dimes are 190 cents
10 quarters are 250 cents
440 total.
