Case Study:
The college has decided to reward our hardworking Math Hub staff with their own break area. They have located a room on the first floor of the 7000 building connected to its own circuit breaker rated at 20 Amps of current. For safety reasons, the hub staff is asked not to exceed 80% of the current rating. The college will provide a small refrigerator rated at 120V/600W, furniture for the break room, and $250 for additional appliances and lighting. The table below lists the other purchases the Hub staff would like to make. Use the information n in this paragraph and the tables below to answer the questions that follow.
Table 1
Item Voltage/Power rating Cost
TV/DVD 120V/240W $300
Coffeemaker 120V/390W $ 45
Toaster Oven 120V/1200W $ 35
Lamp with CFLs 120V/30W $ 20
Table fan 120V/360W $ 25
Clock radio 120V/60W $ 25
Microwave oven 120V/840 $ 99
Q1. The circuit breaker is rated at 20Amps. For safety reasons, the college has asked that the Hub staff not exceed 80% of this rating. What is the maximum amount of current that the Hub break area lighting and appliances can draw? ______________________
Q2. In order to create their break area, the hub staff must make sure that the total current drawn by all of their appliances is less than the maximum you found in question #1. Therefore, you need to calculate how much current each appliance draws. A formula from basic electricity is P = IV. The table below gives further information about each of these variables.
Table 2
Variable Description Unit Unit Abbreviation
P Power Watts W
I Current Amps A
V Voltage Volts V
The rating 120V/360W for the table fan tells us that the table fan must be plugged into a ___________ Volt outlet and will use _________Watts of power.
Q3. Solving P = 1V for 1 gives 1 = ___________
Q4. Using the formula from question #3, the refrigerator provided by the college will draw 1 = 600W divided by 120V = _________ Amps.
Q5. Doing calculations similar to question # 4, determine the current required for each of the other appliances in Table 1.
Q6. After studying the results of table 3, the Hub staff definitely decides to include the refrigerator and the microwave oven. Which of the following selection of appliances could they purchase with the $250 provided by the college?
a) Coffeemaker, clock radio, one lamp
b) Table fan, TV/DVD, one lamp
c) Coffeemaker, two lamps
d) Coffeemaker, table fan, clock radio.
Q7. For each list that was affordable in number 6, determine whether the appliances will exceed the maximum current. Don’t forget to include the refrigerator and microwave in your calculations.
Q8. There is no lighting at all in the break area. The Hub staff decided to go with the refrigerator, the microwave, the coffeemaker, and as many lamps as they can manage without exceeding the maximum current. Write and simplify an inequality that the Math Hub staff can use to determine how many lamps they can have. Let x represent the number of lamps.
Q9. Solve your inequality from # 8. What is the maximum number of lamps that they can place in the break area?
Q10. Find the total cost of the microwave, coffeemaker, and the maximum number of lamps you found in number 9. Will the $250 cover the costs?
Provide complete and step by step solution for the question and show calculations and use formulas.