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

Question

His friend Steve works at a nature tour guide and makes $30 an hour and an additional $20 in tips per day.

(1 point)
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 $
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GPT-4o mini · Answer

Let's break down the information and create the equations step by step.

Ben's Wage Equation: Ben makes $35 per hour. If $ x $ represents the number of hours he works, then his earnings $ y $ can be modeled by the equation: \[ y = 35x \]
Steve's Wage Equation: Steve makes $30 per hour plus an additional $20 in tips. If $ x $ represents the number of hours he works, then his earnings $ y $ can be modeled by the equation: \[ y = 30x + 20 \]
Graphing the Equations: You can input the following equations into Desmos to visualize the graph:
- For Ben: $ y = 35x $
- For Steve: $ y = 30x + 20 $
Finding the Solution: The solution of the system of equations will be the point where the two lines intersect, meaning that at that point, both Ben and Steve earn the same amount. To find their equal earnings, you can solve the equations together:

Setting $ 35x = 30x + 20 $: \[ 35x - 30x = 20 \] \[ 5x = 20 \] \[ x = 4 \]

Now, substitute $ x = 4 $ into either of the equations to find the amount they both make: For Ben: \[ y = 35(4) = 140 \] For Steve: \[ y = 30(4) + 20 = 120 + 20 = 140 \]

Therefore, when they both work 4 hours, they both make $140.