To solve this problem, we can create two equations based on the given information:
Let's define:
x = cost of one cassette
y = cost of one CD
From the first statement, "Two cassettes and three CDs cost $175," we can write the equation:
2x + 3y = 175
From the second statement, "Four cassettes and one CD cost $125," we can write the equation:
4x + y = 125
Now, we have a system of two equations:
2x + 3y = 175 (Equation 1)
4x + y = 125 (Equation 2)
To calculate the cost of one cassette (x), we can solve this system of equations.
One method to solve these equations is by substitution method. We can rearrange Equation 2 to solve for y:
y = 125 - 4x
Now, we substitute this expression for y into Equation 1:
2x + 3(125 - 4x) = 175
Simplifying the equation:
2x + 375 - 12x = 175
-10x = -200
x = (-200)/(-10)
x = 20
Therefore, the cost of one cassette is $20.