Max and Jillian Verde want to make some money over their school\'s spring break.
ID: 3032693 • Letter: M
Question
Max and Jillian Verde want to make some money over their school's spring break. They ask their parents to let them work around the house to earn money. Their parents agree, because Jillian and Max are saving to buy graphing calculators. Dad tells Jillian that he will give her a starting bonus of $10, and then pay her $5 an hour for the work she does around the house. Mom offers Max a slightly different deal. She will give him $40 to start, but only $3 an hour. Write two separate equations - one for Jillian and one for Max - expressing how much money each will earn (including their starting money) in terms of time worked. Graph both equations on the same set of axes. If the graphing calculator costs $72, who will be able to buy a calculator with the least work time? Explain your answer. If the graphing calculator costs $100, who will be able to buy one with the least work time? Explain your answer. For what price must the calculator sell in order for Jillian and Max to earn that amount with the same number of hours of work? Explain your answer.Explanation / Answer
4. Let Jillian and Max work x and y hours respectively , in order to buy the graphing calculator worth $ 100. Then 10+5x = 100 so that 5x = 100- 10 = 90 and x = 90/5= 18. Also, 40 +3y = 100 so that 3y = 100-40 = 60 and y =60/3 = 20. Thus Jillian will be able to buy the graphing calculator with least work time (as 18 < 20).
5. Let Jillian and Max, both work x hours to be able to buy a graphing calculator worth $ y. Then 10+5x = y = 40+3x = y so that 10+5x = 40 +3x or, 40-10 = 5x -3x or, 2x = 30 so that x = 30/2 = 15 hours. Then y = 40+3x = 40+3*15 = 40 +45 = $ 85. We can verify the result by substituting the value of x in the other equation. By doing so, we get 10+5x = 85 or, 10+5*15 = 85 or, 10+75 = 85, which is correct. Hence if the graphing calculator is priced at $ 85, both Jillian and Max can purchase it with 15 hours of work each.