Final answer:
To solve this problem, set up a system of equations with x as the number of quarters and y as the number of dimes. Use substitution to find the values of x and y. The solution is 56 quarters and 29 dimes.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let x represent the number of quarters and y represent the number of dimes. We are given two conditions: Lauren has a total of 85 quarters and dimes, and the total value of the coins is $16.90. We can write the following equations:
x + y = 85 (Equation 1)
0.25x + 0.10y = 16.90 (Equation 2)
To solve this system of equations, we can use substitution or elimination. Let's use substitution here. From Equation 1, we can express x in terms of y: x = 85 - y. Substituting this into Equation 2, we get:
0.25(85 - y) + 0.10y = 16.90
21.25 - 0.25y + 0.10y = 16.90
0.25y - 0.10y = 21.25 - 16.90
0.15y = 4.35
y = 4.35 / 0.15
y = 29
Substituting the value of y back into Equation 1, we solve for x:
x + 29 = 85
x = 85 - 29
x = 56
Therefore, Lauren has 56 quarters and 29 dimes, which corresponds to option A: 55 quarters, 30 dimes.