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We make two sets of equations: x + y = 106 and 0.05x + 0.25y = 13.70. I will solve by substitution. Subtract "x" from both sides of x + y = 106 to convert it to slope intercept form, so y = 106 - x. Substitute y = 106 - x into 0.05x + 0.25y = 13.70, so 0.05x + 0.25(106 - x) = 13.70. Solve for 0.05x + 0.25(106 - x) = 13.70, so 26.5 - 0.2x = 13.7, then x = 64. Substitute 64 into x + y = 106, so 64 + y = 106, then y = 42. There is 64 nickels and 42 quarters.

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