Check it out! 2.1.1: Properties of Equality 1

Sydney subscribes to an online company that allows her to download electronic books. Her subscription costs a flat fee of $30 for up to 10 downloads each month. For each download over 10, there is an additional charge per download. 1.During the month of September, Sydney downloaded 22 books and was charged $75. How much does each additional download cost? 2.In October, Sydney was incorrectly charged $67.50 for 18 books. How much should she have been charged? 3.If Sydney received a bill for $101.25, how many books did she download? 2

1.During the month of September, Sydney downloaded 22 books and was charged $75. Set up an equation to find the charge for each downloaded book over (22 – 10)x = 75 Solve the equation x = 75 Simplify the equation. 12x = 45 Divide both sides by 12. x = 3.75 Each additional download costs $ : Properties of Equality 3

2.In October, Sydney was incorrectly charged $67.50 for 18 books. How much should she have been charged? Set up an equation to find the amount that Sydney should have been charged. The cost for 10 books is $30. Each book over 10 costs an additional $3.75. The total correct cost is (x – 10) : Properties of Equality 4

Total cost = (x – 10) Total cost = (18 – 10) Substitute the number of books she ordered for x. Total cost = (8) Multiply. Total cost = Total cost = 60 The total amount Sydney should have been charged for 18 books is $ : Properties of Equality 5

3.If Sydney received a bill for $101.25, how many books did she download? Use the equation for total cost found earlier to determine the number of books Sydney downloaded. Total cost = (x – 10) = (x – 10) Substitute the value for total cost = x – 37.5 Distribute 3.75 over (x – 10) = 3.75x – 7.5 Combine like terms : Properties of Equality 6

= 3.75x Add 7.5 to both sides of the equation. 29 = x Divide both sides of the equation by The total number of books Sydney downloaded was : Properties of Equality 7