Based on the given information, the number of dimes (x) is 18, and the number of quarters (y) is 31.
How to solve this problem step by step.
Let's assume the number of dimes is represented by the variable "x," and the number of quarters is represented by the variable "y."
The value of dimes is 10 cents each, so the value of x dimes is 10x cents.
The value of quarters is 25 cents each, so the value of y quarters is 25y cents.
According to the given information, the total value of the collection of dimes and quarters is $9.55, which is equal to 955 cents.
Therefore, we can write the first equation:
10x + 25y = 955
Switched coins equation:
According to the second statement, if the quarters were dimes and the dimes were quarters, the total value would be $7.60, which is equal to 760 cents. This gives us the second equation:
25x + 10y = 760
Now, we have a system of two equations with two variables. We can solve this system to find the values of x and y.
Solving the system of equations:
We can use any method to solve the system, such as substitution or elimination. Let's use the elimination method.
Multiply the first equation by 25 and the second equation by 10 to eliminate the variable "y."
250x + 625y = 23875
250x + 100y = 7600
Now, subtract the second equation from the first equation:
625y - 100y = 23875 - 7600
525y = 16275
y = 16275 / 525
y ≈ 31.09
Since the number of coins must be a whole number, we can round down y to the nearest whole number:
y = 31
Substituting this value back into either of the original equations, let's use the first equation:
10x + 25(31) = 955
10x + 775 = 955
10x = 955 - 775
10x = 180
x = 180 / 10
x = 18
Therefore, the number of dimes (x) is 18, and the number of quarters (y) is 31.
To represent this visually, create a graph with x and y as the number of dimes and quarters, respectively.
The x-axis can represent the number of dimes, and the y-axis can represent the number of quarters.
Plotting the point (18, 31) on the graph would represent the solution to the system of equations, where x = 18 and y = 31.