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Answer :
To determine Sakeem's profit when laying sod, we need to create an equation that accounts for both the revenue Sakeem earns per square foot and the cost he incurs per square foot. Here's a step-by-step solution:
1. Identify Costs and Revenue:
- Cost per square foot: Sakeem's supplier charges [tex]$0.43 per square foot for sod.
- Revenue per square foot: Sakeem charges his customers $[/tex]2.00 per square foot to lay the sod.
2. Calculate Profit per Square Foot:
- Profit per square foot is the difference between what Sakeem earns and what he spends for laying each square foot of sod.
- Profit per square foot = Revenue per square foot - Cost per square foot
- Profit per square foot = [tex]$2.00 - $[/tex]0.43 = $1.57
3. Create the Equation for Total Profit:
- The total profit [tex]\( y \)[/tex] Sakeem makes varies directly with the number of square feet of sod [tex]\( x \)[/tex] he lays.
- This means we can use the formula for direct variation: [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of variation (profit per square foot in this case).
- Therefore, the equation becomes: [tex]\( y = 1.57x \)[/tex]
In summary, Sakeem's profit when laying sod is calculated using the equation [tex]\( y = 1.57x \)[/tex], where [tex]\( y \)[/tex] is the total profit and [tex]\( x \)[/tex] is the number of square feet of sod laid.
1. Identify Costs and Revenue:
- Cost per square foot: Sakeem's supplier charges [tex]$0.43 per square foot for sod.
- Revenue per square foot: Sakeem charges his customers $[/tex]2.00 per square foot to lay the sod.
2. Calculate Profit per Square Foot:
- Profit per square foot is the difference between what Sakeem earns and what he spends for laying each square foot of sod.
- Profit per square foot = Revenue per square foot - Cost per square foot
- Profit per square foot = [tex]$2.00 - $[/tex]0.43 = $1.57
3. Create the Equation for Total Profit:
- The total profit [tex]\( y \)[/tex] Sakeem makes varies directly with the number of square feet of sod [tex]\( x \)[/tex] he lays.
- This means we can use the formula for direct variation: [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of variation (profit per square foot in this case).
- Therefore, the equation becomes: [tex]\( y = 1.57x \)[/tex]
In summary, Sakeem's profit when laying sod is calculated using the equation [tex]\( y = 1.57x \)[/tex], where [tex]\( y \)[/tex] is the total profit and [tex]\( x \)[/tex] is the number of square feet of sod laid.
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