SOLUTION: If tom has 3 times as many quarters as dimes and they have a combined value of 340 cents, how many of each coin does he have?

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Question 1077477: If tom has 3 times as many quarters as dimes and they have a combined value of 340 cents, how many of each coin does he have?
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If tom has 3 times as many quarters as dimes and they have a combined value of 340 cents, how many of each coin does he have?
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Each set of 3Q and 1D = 85 cents.
340/85 = 4 sets.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
d = number of dimes
q = number of quarters

10d = value of dimes in terms of cents.
25q = value of quarters in terms of cents.

tom has 3 times as many quarters as dimes.

therefore q = 3d

25q + 10d = 340

since q = 3d, then replace q with its equivalent value of 3d and the equation becomes:

25 * (3d) + 10d = 340

simplify to get:

75d + 10d = 340

combine like terms to get:

85d = 340

solve for d to get d = 340 / 85 = 4

since q = 3d, then q = 12

tom has 12 quarters and 4 dimes for a total of 12 * 25 + 4 * 10 = 340 cents.

what you are doing is using the concept of equivalent values to reduce the number of unknown variables so you can solve the equation.

since q equals the number of quarters and d equal the number of dimes, and since the number of quarters is equal to three times the number of dimes, you set up the equivalent value of q = 3d.

you then replace q with the equivalent value of 3d in the equation to solve for d.