Algebra 1 Section 3.6

An understanding of the proper use of money is important to living the godly life that is expected of a Christian.

Definitions The cost is the amount a merchant pays for the merchandise he will sell. The markup is the amount the merchant adds to his cost to arrive at the retail price.

Definitions The markup rate is the amount of markup on an item as a percent of its cost. markup = markup rate × cost cost + markup = retail price

Definitions The retail price is the merchant’s cost plus markup; it is the regular amount a merchant asks his customer to pay for merchandise.

Definitions The discount rate is the percent by which the retail price is reduced. The discount is the amount by which the retail price is reduced.

Definitions The sale price is the customer’s cost after the retail price has been discounted. discount = discount rate × retail price retail price – discount = sale price

Example 1 markup = markup rate × cost markup = 0.75(15) = 11.25 cost + markup = retail price 15 + 11.25 = $26.25

Example 1 Or...you can do it this way: retail price = cost + 0.75(cost) = (1 + 0.75)(cost) = 1.75(cost) = 1.75(15) = $26.25

Example 2 discount rate × retail price = discount 0.3r = 52.50 52.5 0.3 r = = $175 sale price = retail price – discount = 175 – 52.50 = $122.50

Example 2 Or...you can do it this way: sale price = retail price – discount = retail price – (discount rate) (retail price) = retail price – 0.3(retail price) = 0.7(retail price)

Definitions A tip is the amount paid for a personal service. tip rate × total bill = tip

Definitions Commission is the dollar amount an employee receives as a result of the sales he makes.

Definitions The rate is the percent used to determine a tip or commission based on the amount of the bill or an employee’s sales. commission rate × sales = commission

Example 4 salary + commission rate × sales = commission 2175 + 8250r = 3660 8250r = 1485 1485 8250 r = = 0.18 r = 18%

Simple Interest I = Prt I = amount of simple interest P = principal invested/borrowed r = annual interest rate (decimal) t = time (years)

$300 was invested in each account. Example 5 P r t = I 1st 2nd x 0.05 0.07 1 = 0.05x 0.07x 12x = 3600 x = 300 $300 was invested in each account. 0.05x + 0.07x = 36 5x + 7x = 3600

Note that x is in years, not months! Example 6 P r t = I 6% 8% 500 900 0.06 0.08 x x – 0.25 = 500(0.06)x 900(0.08)(x – 0.25) 30x 72(x – 0.25) Note that x is in years, not months! x = 0.5 (years) x = 6 months

Example 6 x = 6 months The $500 loan was for 6 mo.

Percent Formulas Percent × Whole = Part Markup Rate × Cost = Markup Discount Rate × Retail Price = Discount Tip Rate × Total Bill = Tip

Percent Formulas Commission Rate × Sales = Commission Principal × Rate × Time = Interest

Homework: pp. 126-128