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A number of dimes and quarters are worth $2.55. If the number od dimes and quarters were interchanged the resulting new amount would be $2.70. How many of each kind of coin were there before the interchange?

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Answer:

8 dimes

7 quarters

Step-by-step explanation:

Let number of

Dimes = x ; quarters = y

10x + 25y = 255 ___(1)

25x + 10y = 270 ___(2)

From (1)

10x = 255 - 25y

x = (255 - 25y) / 10

x = 25.5 - 2.5y

Put x = 25.5 - 2.5y in (2)

25(25.5 - 2.5y) + 10y = 270

637.5 - 62.5y + 10y = 270

-52.5y = - 367.5

y = 367.5 / 52.5

y = 7

x = 25.5 - 2.5(7)

x = 25.5 - 17.5

x = 8

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