Willow bought 3 m of denim fabric and 5 m of cotton fabric. The
total bill, excluding tax, was $22. Jared bought 6 m of denim fabric
and 2 m of cotton fabric at the same store for $28.
a) Write a linear system you can solve to determine the price
of denim fabric and the price of cotton fabric.
b) Solve your system using a graph.
c) How much will 8 m of denim fabric and 5 m of cotton fabric cost?
Let's assign variables to represent the price of denim fabric and cotton fabric.
Let d be the price per meter of denim fabric in dollars.
Let c be the price per meter of cotton fabric in dollars.
From the given information, we can set up the following system of equations:
1) 3d + 5c = 22 (equation from Willow's purchase)
2) 6d + 2c = 28 (equation from Jared's purchase)
To solve the system using a graph, we can plot the lines represented by these equations and find their point of intersection. The coordinates of the intersection point will give us the prices of denim and cotton fabrics.
Let's graph the equations:
Equation 1: 3d + 5c = 22
Let's rewrite this equation in terms of c:
c = (22 - 3d)/5
Equation 2: 6d + 2c = 28
Let's rewrite this equation in terms of c:
c = (28 - 6d)/2
Graphing both equations, we get:
Graph: https://www.desmos.com/calculator/qeyorw2yug
From the graph, we can see that the intersection point is approximately (d = 4, c = 2). Therefore, the price of denim fabric is $4 per meter, and the price of cotton fabric is $2 per meter.
To find the cost of purchasing 8 m of denim fabric and 5 m of cotton fabric, we can substitute these values into the price per meter in the original equations:
Cost of 8 m of denim fabric = 8 * $4 = $32
Cost of 5 m of cotton fabric = 5 * $2 = $10
Therefore, the total cost of 8 m of denim fabric and 5 m of cotton fabric would be $32 + $10 = $42.