To cut a lawn, allan charges a fee of $15 for his equipment and $8.50 per hour spent cutting a lawn. taylor charges a fee of $12 for his equipment and $9.25 per hour spent cutting a lawn. if x represents number of hours spent cutting a lawn, what are all values of x for which taylor's total charge is greater than allan's total charge?

Algebraic equations are equations with unknown variables. These unknown variables can be represented using the alphabet.

All values of x for which Taylor's total charge is greater than Allan's total charge is given as x > 4

Let's represent the number of hours Allan and Taylor spent cutting grass as : h

From the question, we are told that

Allan charges a fee of $15 for his equipment and $8.50 per hour spent cutting a lawn.

The algebraic equation for Allan is given as :

$15 + $8.50 × x

15 + 8.5x Equation 1

Taylor charges a fee of $12 for his equipment and $9.25 per hour spent cutting a lawn.

The algebraic equation for Taylor is given as :

$12 + $9.25 × x

12 + 9.25x Equation 1

To find all values of x for which Taylor's total charge is greater than Allan's total charge we would equate both equations to each other using the inequality sign ">"

Equation 2 > Equation 1

12 + 9.25x > 15 + 8.5x

Collect like terms

9.25x - 8.5x > 15 - 12

0.75x > 3

Divide both sides by 0.75

0.75x / 0.75 > 3/ 0.75

x  > 4

Therefore, all values of x for which Taylor's total charge is greater than Allan's total charge is given as x > 4

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x > 4

Step-by-step explanation:

First I made an equation to find the cost for each Allen and Taylor.

Allen : 15 + 8.50x

Taylor = 9.25x + 12

Now that we know the equations we can set up an inequality.

9.25x+12>8.5x+15

Now you can solve!

Step 1: Subtract 8.5x from both sides.

9.25x+12−8.5x>8.5x+15−8.5x

0.75x+12>15

Step 2: Subtract 12 from both sides.

0.75x+12−12>15−12

0.75x>3

Step 3: Divide both sides by 0.75.

x > 4

x+14

step-by-step explanation: