An equation is formed when two equal expressions. The number of dimes and nickels in Caroline's purse is 12 and 27, respectively.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of dimes in Caroline's purse be represented by x, while the number of nickels is represented by y.
Given that the number of nickels is nine less than three times the number of dimes. Therefore, we can write,
y = 3x - 9
Also, Caroline has a total of $2.55 in her purse. Therefore, we can write,
0.10x + 0.05y = 2.55
Substitute the value of y from the above equation,
0.10x + 0.05(3x - 9) = 2.55
0.10x + 0.15x - 0.45 = 2.55
0.25x = 2.55 + 0.45
0.25x = 3
x = 3/0.25
x = 12
Substitute the value of x in the equation of y,
y = 3x - 9
y = 3(12) - 9
y = 36 - 9
y = 27
Hence, the number of dimes and nickels in Caroline's purse is 12 and 27, respectively.
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