Questions: A landscaping company charges 48 per cubic yard of mulch plus a delivery charge of 29. Find a linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch. C(x)=

A landscaping company charges 48 per cubic yard of mulch plus a delivery charge of 29. Find a linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch. C(x)=
Transcript text: A landscaping company charges $\$ 48$ per cubic yard of mulch plus a delivery charge of $\$ 29$. Find a linear function which computes the total cost C (in dollars) to deliver $\boldsymbol{x}$ cubic yards of mulch. \[ C(x)= \]
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Solution

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Solution Steps

To find the linear function that computes the total cost \( C \) for delivering \( x \) cubic yards of mulch, we need to consider both the cost per cubic yard and the fixed delivery charge. The cost per cubic yard is $48, and the delivery charge is a constant $29. Therefore, the total cost function can be expressed as a linear equation where the slope represents the cost per cubic yard and the y-intercept represents the delivery charge.

Step 1: Define the Linear Function

The total cost \( C(x) \) for delivering \( x \) cubic yards of mulch can be expressed as a linear function. The cost per cubic yard is $48, and there is a fixed delivery charge of $29. Therefore, the linear function is:

\[ C(x) = 48x + 29 \]

Step 2: Calculate the Total Cost for 5 Cubic Yards

To find the total cost for delivering 5 cubic yards of mulch, substitute \( x = 5 \) into the linear function:

\[ C(5) = 48 \times 5 + 29 \]

Step 3: Perform the Calculation

Calculate the expression:

\[ C(5) = 240 + 29 = 269 \]

Final Answer

The total cost to deliver 5 cubic yards of mulch is \(\boxed{269}\) dollars.

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