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Answer :
To solve this problem, we're going to create an equation to find Sakeem's profit from laying sod. We know that Sakeem's profit varies directly with the number of square feet of sod he lays.
Here’s a step-by-step guide to forming the equation:
1. Identify Sakeem's Charges and Costs:
- Sakeem charges his customers [tex]$2.00 per square foot for laying sod.
- His supplier charges $[/tex]0.43 per square foot for the sod.
2. Calculate the Profit per Square Foot:
- Profit is calculated by subtracting the cost per square foot from the charge per square foot.
- So, the profit per square foot is:
[tex]\[
\text{Profit per square foot} = \text{charge per square foot} - \text{cost per square foot}
\][/tex]
- Numerically, this is:
[tex]\[
\text{Profit per square foot} = 2.00 - 0.43 = 1.57
\][/tex]
3. Formulate the Profit Equation:
- The total profit [tex]\( y \)[/tex] Sakeem makes depends on the total number of square feet of sod he lays, represented by [tex]\( x \)[/tex].
- Since profit varies directly as the number of square feet, the equation will be of the form:
[tex]\[
y = 1.57x
\][/tex]
- Here, [tex]\( y \)[/tex] represents the total profit, and [tex]\( x \)[/tex] is the number of square feet of sod laid.
This equation, [tex]\( y = 1.57x \)[/tex], perfectly represents Sakeem's profit where [tex]$1.57$[/tex] is the profit per square foot and [tex]\( x \)[/tex] is the number of square feet laid. This allows Sakeem to calculate his profit easily for any size lawn he works with.
Here’s a step-by-step guide to forming the equation:
1. Identify Sakeem's Charges and Costs:
- Sakeem charges his customers [tex]$2.00 per square foot for laying sod.
- His supplier charges $[/tex]0.43 per square foot for the sod.
2. Calculate the Profit per Square Foot:
- Profit is calculated by subtracting the cost per square foot from the charge per square foot.
- So, the profit per square foot is:
[tex]\[
\text{Profit per square foot} = \text{charge per square foot} - \text{cost per square foot}
\][/tex]
- Numerically, this is:
[tex]\[
\text{Profit per square foot} = 2.00 - 0.43 = 1.57
\][/tex]
3. Formulate the Profit Equation:
- The total profit [tex]\( y \)[/tex] Sakeem makes depends on the total number of square feet of sod he lays, represented by [tex]\( x \)[/tex].
- Since profit varies directly as the number of square feet, the equation will be of the form:
[tex]\[
y = 1.57x
\][/tex]
- Here, [tex]\( y \)[/tex] represents the total profit, and [tex]\( x \)[/tex] is the number of square feet of sod laid.
This equation, [tex]\( y = 1.57x \)[/tex], perfectly represents Sakeem's profit where [tex]$1.57$[/tex] is the profit per square foot and [tex]\( x \)[/tex] is the number of square feet laid. This allows Sakeem to calculate his profit easily for any size lawn he works with.
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