Danielle and David each have a job. Danielle earns $15 an hour. She also receives a $50 weekly bonus. Danielle wrote an equation
to determine how much she earns in a given week. y=15x+50y=15x+50 David earns $12 an hour and receives an $80 weekly bonus. David made a graph to show how much he earns in a given week. How many hours will it take Danielle and David to earn the same amount of money? Enter your answer in the box below.
For starters, create an equation to show David's earnings. We can do this using Danielle's as a basis, which is set up as y=(# of hours)x+(bonus). This gives us y=12x+80. Now, as we need both their ys to be equal, we just set both equations equal to each other, making 15x+50=12x+80. Now, we solve for x, starting with 15x+50=12x+80, subtracting 12x from both sides to get 3x+50=80, subtracting 50 from both sides to get 3x=30, and dividing three from both sides to get x=10. To check, we just plug in our answer to both equations and see if the ys match up. With Danielle's equation, we get y=15(10)+50=150+50=200 and with David's equation, we get y=12(10)+80=120+80=200, proving that our answer is correct.
