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Answer :
To determine Sakeem's profit when he lays sod, we need to create an equation based on the information given. Here's how you can approach the problem step by step:
1. Understand the Key Concepts:
- Sakeem is charged [tex]$0.43 per square foot by his supplier for the sod.
- He charges his customers $[/tex]2.00 per square foot to install the sod.
- Profit is calculated as the difference between what he charges and what it costs him.
2. Calculate the Profit Per Square Foot:
- The amount Sakeem charges per square foot is [tex]$2.00.
- The cost per square foot is $[/tex]0.43.
- Therefore, the profit he makes per square foot is calculated by subtracting the cost from the charge:
[tex]\[
\text{Profit per square foot} = 2.00 - 0.43 = 1.57
\][/tex]
3. Set Up the Equation:
- Let [tex]\( y \)[/tex] represent the total profit.
- Let [tex]\( x \)[/tex] represent the number of square feet of sod laid.
- Since the profit varies directly with the number of square feet, the equation for total profit becomes:
[tex]\[
y = 1.57 \times x
\][/tex]
This is the equation that shows Sakeem's profit when laying sod: [tex]\( y = 1.57x \)[/tex]. Here, [tex]\( 1.57 \)[/tex] is the constant of variation, representing the profit per square foot.
1. Understand the Key Concepts:
- Sakeem is charged [tex]$0.43 per square foot by his supplier for the sod.
- He charges his customers $[/tex]2.00 per square foot to install the sod.
- Profit is calculated as the difference between what he charges and what it costs him.
2. Calculate the Profit Per Square Foot:
- The amount Sakeem charges per square foot is [tex]$2.00.
- The cost per square foot is $[/tex]0.43.
- Therefore, the profit he makes per square foot is calculated by subtracting the cost from the charge:
[tex]\[
\text{Profit per square foot} = 2.00 - 0.43 = 1.57
\][/tex]
3. Set Up the Equation:
- Let [tex]\( y \)[/tex] represent the total profit.
- Let [tex]\( x \)[/tex] represent the number of square feet of sod laid.
- Since the profit varies directly with the number of square feet, the equation for total profit becomes:
[tex]\[
y = 1.57 \times x
\][/tex]
This is the equation that shows Sakeem's profit when laying sod: [tex]\( y = 1.57x \)[/tex]. Here, [tex]\( 1.57 \)[/tex] is the constant of variation, representing the profit per square foot.
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