MAT143 Lab 2 Study Notes

MAT143 Lab 2 Central Piedmont Community College 1. A coffee and a Danish from a local café costs $6.15 plus a 6.25% tax. How much would a person spend on a breakfast coffee and Danishes if they purchased this meal twice a week for a year (52 weeks)? $679.12 Cost before tax $6.15 13.06 a week x52= 679.12 for the year Cost After tax $6.53 x 2 = 13.06 2. True or False: A shirt is on sale for 40% off, and you have an additional 20% off coupon. The shirt will ultimately be 60% off the original price. If false, explain. False. That is 20% of $60 = =$12 The 20% discount amount 20x60/100= $12 Final price of the shirt = $60-$12=$48 The ultimately the shirt will be 100 - 48/100 = 52% off the original price. 3. Use the table to answer the following questions. US Dollar Exchange Rates US Dollar (USD) Units per USD USD per Unit British Pound 0.711579 1.405332 a. What is the unit exchange rate of US dollars to British pounds? 1 US Dollar = 0.711579 b. What is the unit exchange rate of British Pounds to US dollars? 1 British Pound = 1.405332 US Dollars c. If a pair of shoes cost 75 US dollars, approximately how many British Pounds do the shoes cost? 1 US Dollar = 0.711579 British Pounds 75 US Dollar = 75 x 0.711579 British Pounds 53.37 British Pounds =53 British Pounds 4. A French recipe for Pain au Chocolat calls for 120 mL of milk and needs the oven preheated to 190℃. You only have measuring cups in fluid ounces and Fahrenheit on your oven temperature dial. Determine the amount of milk needed in fluid ounces and temperature for the oven in Fahrenheit. Round your answer to the nearest tenth, if necessary. (Note: There are 8 fluid ounces per cup) Milk: 120ml Temperature:190 degrees celsius 1 fluid ounce = 29.5735mL 120mL x 1fl oz/29.5735mL = 4.06 fl oz F = ( C x 1.8) + 32 F = ( 190 x 1.8) + 32 = 374 degrees fahrenheit 4.06 fluid ounces each mL 374 degrees Fahrenheit 5. The following table shows the area of apartments along with the monthly rent. Apartment Rent Area (square feet) Price (dollars) 504 1450 723 2180 465 1040 812 1970 389 930 637 1320 558 1290 a. Use the apartment with the smallest area and the apartment with the largest area to create a linear equation that can be used to estimate the price of rent based on the area. Let x be the area and y be the price. y (x) y - 930 = (1,970 - 930/ 812 - 389) (x- 389) y - 930 = (1,040/423) (x - 389) y - 930 = 2.4586x - 956.4066 y - 930 = 2.4586x - 956.4066 + 930 Answer: y(x) = 2.4586x - 26.4066 b. Use this equation to estimate the price a landlord should use to rent out an apartment with an area of 500 square feet. Round your answer to the nearest cent. y (x) = 2.4586 - 26.4066 y (500) = 2.4586 x 504 - 26.4066 = $1,202.89 dollars The price to rent an area of x = 500 square feet is $1,202.89 c. How does the price obtained from the formula compare to the apartment that is 504 square feet? Explain why the prices might be similar or different. Price is dependent on location. The Price to rent of area x = 504 square feet is 1,212.73. According to the table it will cost $1,450. 6. Suppose you want to borrow $50 from either your brother or your sister for a week. They each odder you a different condition for borrowing money. Your brother asks for an additional $5 for each day that you are late paying back the money. Your sister says she will increase the total amount you owe her by 10% for each day you are late returning the money. Your brother and sister both want the full amount paid back all at once. a. Create a function model for the money you need to return to your brother based on the number of days you are late paying back the money. Total Amount = 50 + 5x = 5x + 50 b. Create a function model for the money you need to return to your sister based on the number of days you are late paying back the money. Y = 50 (1 + 10/100)x The X outside of the parenthesis is an exponent y= 50 (1 + 1/10) x y= 50 ( 10 + 1/10)x y= 50 (11/10)x y= 50(1.1)x c. How much money do you need to return in both cases if you are 3 days late in paying back the money? Brother = $65 = 5(x) + 50 = 5 x 3 + 50 = 15 + 50 = 65 Sister = $66.55 50(1.1)x 50(1.1)3 50 (1.331) =66.55 d. If you knew that you would be at least 2 days late paying back the money, who would you borrow money from? The Brother because it is 55 cents cheaper than the sister.