SOLUTION: Mike said " guess how many coins and dollar bills I have in my pocket. Their value is $13.40, and I have three times as many quarters as dimes. How many of each coin do I have?"

Question 527199: Mike said " guess how many coins and dollar bills I have in my pocket. Their value is $13.40, and I have three times as many quarters as dimes. How many of each coin do I have?"
Found 2 solutions by oberobic, MathTherapy:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
With coin problems, you have to keep track of the count of coins and their values.
d = number of dimes
10d = value of dimes in cents
q = number of quarters
25q = value of quarters in cents
.
10d + 25q = 1340 cents
.
Mike has 3 time as many quarters as dimes, so we would state
.
q = 3d
.
10d +25(3d) = 1340
.
10d + 75d = 1340
.
85d = 1340
.
d = 1340/85
.
At this point, the problem is that 1340/85 is not an integer.
.
Since you cannot have fractional dimes, you have to successively determine the point where you get an integer from the division. You can do this by subtracting 100 cents (1 dollar) again and again. Or you might notice that 85*4 = 170*2 = 340.
.
That would mean Mike has 10 $1 bills in his pocket, 4 dimes and 12 quarters.
.
Check the solution to determine if it is the answer.
25(12) = 300 cents
10(4) = 40 cents
10 * 100 = 1000 cents
300 + 40 + 1000 = 1340 cents = $13.40
.
Done.
Answer by MathTherapy(10553) (Show Source): You can put this solution on YOUR website!
Mike said " guess how many coins and dollar bills I have in my pocket. Their value is $13.40, and I have three times as many quarters as dimes. How many of each coin do I have?"

Let amount of dimes be C, and amount of dollar bills, D
Then amount of quarters = 3C

Since we have $0.40, there MUST be at least 4 dimes, because a quarter and dimes DO NOT MAKE $0.40

Trying 4 dimes, we have:

.1C + .25(3C) + D = 13.4

.1C + .75C + D = 13.4

.1(4) + .75(4) + D = 13.4

.4 + 3 + D = 13.4

D, or amount of dollar bills = 13.4 - .4 � 3, or 10
This means that there are:
, with dollar value of $0.40

, with dollar value of $3.00

, with dollar value of $10.00

-------
Check
-------

$0.40 + $3.00 + $10.00 = $13.40

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