Final answer:
Sharon has 9 dimes and 43 nickels.
Step-by-step explanation:
To model this situation, we can use a system of equations. Let's say Sharon has 'd' dimes and 'n' nickels. From the given information, we know that she has a total of 52 coins, so we can write the equation: d + n = 52. We also know that the value of the coins is $3.05, which can be represented as 10d + 5n = 305 cents.
To solve this system of equations, we can use substitution or elimination. Let's use elimination. Multiply the first equation by 10 to get 10d + 10n = 520. Subtract this equation from the second equation to eliminate 'd': (10d + 5n) - (10d + 10n) = 305 - 520. Simplify: -5n = -215. Divide by -5: n = 43. Substitute this value of 'n' into the first equation to find 'd': d + 43 = 52. Subtract 43 from both sides: d = 9.
Therefore, Sharon has 9 dimes and 43 nickels.