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Ben works as a park ranger and makes $35 an hour.

His friend Steve works at a nature tour guide and makes $30 an hour and an additional $20 in tips per day.
1) Write an equation that represents Ben's wage. Let x represent the number of hours he works and y represent how much he earns.

2) Write an equation that represents Steve's wage. Let x represent the number of hours he works and y represent how much he earns.

3) Graph this system of equations into Desmos. Click here to open Desmos.

4) The solution of the system of equations means that when they both work
hours, they both make $

Answer 1

1. For Ben's wage, the equation can be written as: \[ y = 35x \] where \( y \) is the amount he earns and \( x \) is the number of hours he works.

2. For Steve's wage, the equation can be written as: \[ y = 30x + 20 \] where \( y \) is the amount he earns (including tips) and \( x \) is the number of hours he works.

3. To graph these equations in Desmos, you would input the two equations:

• For Ben: \( y = 35x \)
• For Steve: \( y = 30x + 20 \)

4. The solution of the system of equations represents the number of hours they work, at which point both Ben and Steve have the same earnings. To find this, you can set their wage equations equal to each other: \[ 35x = 30x + 20 \] Solving for \( x \): \[ 35x - 30x = 20 \] \[ 5x = 20 \] \[ x = 4 \]

Plugging the value \( x = 4 \) back into either equation to find out how much they make: Using Ben's equation: \[ y = 35(4) = 140 \]

So when they both work 4 hours each, they both make $140.