Two cassettes and three cd's cost $175 while four cassettes and one cd cost $125.
1)Given that one cassette cost $x and one cd cost $y,write two equations in x and y to represent this information.
2)Calculate the cost of one cassette.
1. just translate the English into Math
"Two cassettes and three cd's cost $175" ---> 2x + 3y = 175
"four cassettes and one cd cost $125" ---> 4x + y = 125
2. double the first equation
4x + 6y = 350 then subtract the second
4x + y = 125
-------------
5y = 225
y = 45
back in the second
4x + 45 = 125
4x = 80
x = 20
(expensive cassettes and CDs)
2x+3y
Calculate the cost of 1CD
1) Let's create the equations based on the given information:
- Equation 1: 2x + 3y = 175 (Two cassettes and three CDs cost $175)
- Equation 2: 4x + y = 125 (Four cassettes and one CD cost $125)
2) To calculate the cost of one cassette, we can rearrange Equation 1 to solve for x:
2x + 3y = 175
2x = 175 - 3y
x = (175 - 3y)/2
Now, substitute the value of x in Equation 2:
4(175 - 3y)/2 + y = 125
2(175 - 3y) + y = 125
350 - 6y + y = 125
-5y = -225
y = 45
So, the cost of one cassette is $45.
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.