To cut a lawn, Antwan charges a fee of 10.00 for his equipment and 8.50 per hour spent cutting a lawn. Taylor charges a fee of 7.00 for her equipment and 9.50 per hour spent cutting a lawn. If x represents the number of hours spent cutting a lawn, what are all the values of x for which Taylor's total charge is greater than Antwan's total charge?

To cut a lawn, Antwan charges a fee of 10.00 for his equipment and 8.50 per hour spent... | SAT Linear inequalities in one or two variables Practice

Answer: D. $x>3$

Explanation:1. Define the total charge for Antwan: Antwan charges a fee of $ $10.00$ for equipment and $ $8.50$ per hour ( $x$ ). Antwan's total charge, $C\_A = 10.00 + 8.50x$ .

Define the total charge for Taylor: Taylor charges a fee of $ $7.00$ for equipment and $ $9.50$ per hour ( $x$ ). Taylor's total charge, $C\_T = 7.00 + 9.50x$ .
Set up the inequality: We want to find the values of $x$ for which Taylor's total charge is greater than Antwan's total charge. $C\_T > C\_A$ $7.00 + 9.50x > 10.00 + 8.50x$
Solve the inequality for $x$ : Subtract $8.50x$ from both sides: $7.00 + 9.50x - 8.50x > 10.00 + 8.50x - 8.50x$ $7.00 + 1.00x > 10.00$ Subtract $7.00$ from both sides: $1.00x > 10.00 - 7.00$ $1.00x > 3.00$ $x > 3$
Compare with the given options: [A] $2 \le x \le 3$ [B] $3 \le x \le 4$ [C] $x<2$ [D] $x>3$ Our result matches option D.
Conclusion: Taylor's total charge is greater than Antwan's total charge for $x>3$ hours.

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SAT Linear inequalities in one or two variables practice question

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