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Answer :
To solve the problem of finding Sakeem's profit when laying sod, we need to create an equation that represents how his profit varies directly with the number of square feet of sod he lays.
Step 1: Understand the Problem
- Sakeem's supplier charges \[tex]$0.43 per square foot for sod.
- Sakeem charges his customers \$[/tex]2.00 per square foot.
- "Profit" is defined as the amount earned minus the amount spent.
Step 2: Calculate Profit Per Square Foot
To determine how much profit Sakeem makes per square foot, we subtract the cost from the charge:
[tex]\[ \text{Profit per square foot} = \text{Charge per square foot} - \text{Cost per square foot} \][/tex]
[tex]\[ \text{Profit per square foot} = 2.00 - 0.43 \][/tex]
[tex]\[ \text{Profit per square foot} = 1.57 \][/tex]
Step 3: Write the Variation Equation
Using the fact that the profit varies directly with the number of square feet, let:
- [tex]\( y \)[/tex] be the total profit.
- [tex]\( x \)[/tex] be the number of square feet of sod.
The equation that represents this direct variation is:
[tex]\[ y = 1.57 \times x \][/tex]
This equation illustrates that Sakeem makes a profit of \$1.57 for every square foot of sod he lays. Therefore, his total profit [tex]\( y \)[/tex] is calculated by multiplying 1.57 by the number of square feet [tex]\( x \)[/tex].
Step 1: Understand the Problem
- Sakeem's supplier charges \[tex]$0.43 per square foot for sod.
- Sakeem charges his customers \$[/tex]2.00 per square foot.
- "Profit" is defined as the amount earned minus the amount spent.
Step 2: Calculate Profit Per Square Foot
To determine how much profit Sakeem makes per square foot, we subtract the cost from the charge:
[tex]\[ \text{Profit per square foot} = \text{Charge per square foot} - \text{Cost per square foot} \][/tex]
[tex]\[ \text{Profit per square foot} = 2.00 - 0.43 \][/tex]
[tex]\[ \text{Profit per square foot} = 1.57 \][/tex]
Step 3: Write the Variation Equation
Using the fact that the profit varies directly with the number of square feet, let:
- [tex]\( y \)[/tex] be the total profit.
- [tex]\( x \)[/tex] be the number of square feet of sod.
The equation that represents this direct variation is:
[tex]\[ y = 1.57 \times x \][/tex]
This equation illustrates that Sakeem makes a profit of \$1.57 for every square foot of sod he lays. Therefore, his total profit [tex]\( y \)[/tex] is calculated by multiplying 1.57 by the number of square feet [tex]\( x \)[/tex].
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