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 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 $

Question

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 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 $​​​​​​​

GPT-4o mini · Answer

1) For Ben's wage, we can express his earnings $ y $ based on the number of hours $ x $ he works. The equation for Ben's wage is: $$ y = 35x $$ 2) For Steve's wage, he makes $30 per hour and also earns an additional $20 in tips per day. Therefore, Steve's total earnings $ y $ can be expressed as: $$ y = 30x + 20 $$ 3) To graph these equations using Desmos, you would go to the Desmos graphing calculator and enter the following equations: - For Ben: $ y = 35x $ - For Steve: $ y = 30x + 20 $ This will allow you to visualize how much each of them earns based on the number of hours they work. 4) The solution of the system of equations represents the number of hours they both work at which their earnings are equal. To find this, you would set the two equations equal to each other: $$ 35x = 30x + 20 $$ Solving this gives: $$ 5x = 20 $$ $$ x = 4 $$ At $ x = 4 $ hours, you can substitute back into either equation to find the earnings: $$ y = 35(4) = 140 \quad \text{(for Ben)} $$ $$ y = 30(4) + 20 = 120 + 20 = 140 \quad \text{(for Steve)} $$ Therefore, when they both work 4 hours, they both make **$140**.