Final answer:
Rose has $1.35 in nickels and quarters with nine more nickels than quarters. By setting up and solving a system of equations, we find that she has 4 quarters and 13 nickels.
Step-by-step explanation:
Rose counted her money and found that she had $1.35 in nickels and quarters. There are nine more nickels than quarters. To solve how many of each coin Rose has, we set up two equations. Let n represent the number of nickels and q represent the number of quarters.
Since each nickel is worth 5 cents (or $0.05) and each quarter is worth 25 cents (or $0.25), and the total value is $1.35, we can write the first equation as:
0.05n + 0.25q = 1.35
Given that there are nine more nickels than quarters, we write the second equation as:
n = q + 9
Now, we can solve the system of equations. First, replace n in the first equation with q + 9:
0.05(q + 9) + 0.25q = 1.35
After simplifying and solving for q, we find that q (the number of quarters) is 4 and n (the number of nickels) is 13. Hence, Rose has 4 quarters and 13 nickels.