Questions: Sakeem is a landscape architect. When he creates a lawn, his supplier charges 0.43 per 5 square foot for sod. Sakeem charges his customers 2.00 per square foot to lay the sod. The profit Sakeem makes when creating a lawn varies directly as the number of square feet of sod he lays. Create an equation to show Sakeem's profit when laying sod, where y is the profit and x is the number of square feet of sod. Recall that profit is the difference of the amount earned and the amount spent.

Sakeem is a landscape architect. When he creates a lawn, his supplier charges 0.43 per 5 square foot for sod. Sakeem charges his customers 2.00 per square foot to lay the sod. The profit Sakeem makes when creating a lawn varies directly as the number of square feet of sod he lays.

Create an equation to show Sakeem's profit when laying sod, where y is the profit and x is the number of square feet of sod. Recall that profit is the difference of the amount earned and the amount spent.

Transcript text: Sakeem is a landscape architect. When he creates a lawn, his supplier charges $\$ 0.43$ per $5$ square foot for sod. Sakeem charges his customers $\$ 2.00$ per square foot to lay the sod. The profit Sakeem makes when creating a lawn varies directly as the number of square feet of sod he lays. Create an equation to show Sakeem's profit when laying sod, where $y$ is the profit and $x$ is the number of square feet of sod. Recall that profit is the difference of the amount earned and the amount spent.

Solution

Solution Steps

To create an equation for Sakeem's profit, we need to calculate the difference between the revenue he earns from laying sod and the cost he incurs for purchasing the sod. The revenue is calculated by multiplying the charge per square foot by the number of square feet, and the cost is calculated by multiplying the cost per square foot by the number of square feet. The profit is then the revenue minus the cost.

Step 1: Define the Variables

Let $ x $ be the number of square feet of sod Sakeem lays. The profit $ y $ is the difference between the revenue and the cost.

Step 2: Calculate Revenue

The revenue Sakeem earns is calculated by multiplying the charge per square foot by the number of square feet: \[ \text{Revenue} = 2.00 \times x \]

Step 3: Calculate Cost

The cost Sakeem incurs is calculated by multiplying the cost per square foot by the number of square feet: \[ \text{Cost} = 0.43 \times x \]

Step 4: Calculate Profit

The profit $ y $ is the difference between the revenue and the cost: \[ y = (2.00 \times x) - (0.43 \times x) = (2.00 - 0.43) \times x = 1.57 \times x \]

Step 5: Substitute the Given Value

Substitute $ x = 1000 $ into the profit equation: \[ y = 1.57 \times 1000 = 1570 \]