These are the solutions to the percent exercises. You are strongly advised to work out your own solutions before you look at these.
Suppose the deal of the day at Amazon.com is a lady's watch being sold for $49.99. If the list price is $125, what is the rate of discount? If the buyer must pay 6% sales tax plus $5.97 for shipping and handling, what will be the final cost to the buyer?
change = vnew - vold = 49.99 - 125 = -$75.01 discount r = change/vold = -75.01/125 = -0.60008 ≈ -60% = 60% off tax = change = rvold = 0.06 * 49.99 ≈ $3.00 tax final cost = 49.99 + 3.00 + 5.97 = $58.96 final cost
Notice that the interpretation of vold changes in this problem because there are two different contexts. When calculating the discount rate, the original (old) value is the list price of $125 but when calculating the tax, the original (old) value is the sale price of $49.99.
While on a diet, a woman's weight goes from 160 to 130 pounds. Express her weight loss as a percent.
change = vnew - vold = 130 - 160 = -30 = 30 pound weight loss r = change/vold = -30/160 = -0.1875 = -18.75% = 18.75% weight loss
Suppose the woman in the previous exercise gained back all of the weight she had lost (an all too common occurrence). Express her weight gain as a percent.
change = vnew - vold = 160 - 130 = 30 pound weight gain
r = change/vold = 30/130 = 0.2307692308 = ≈ 23.08% weight gain
The invoice price of a car is the price the car dealer pays to buy the car from the manufacturer. The invoice price represents the cost of making the car plus a markup (the manufacturer's profit). Suppose the invoice price for a Chevy Malibu is $21,636. What does it cost to make this car if the manufacturer's markup is 10%?
vnew = vold + change = vold + rvold = vold(1 + r)
implies vold = vnew/(1 + r) = 21636/(1 + 0.10) = 21636/1.1 ≈ $19,669
It cost the manufacturer about $19,669 to make the Chevy Malibu.
A car's sticker price is the manufacturer's suggested retail price (MSRP). If the invoice price for a Chevy Malibu is $21,636 and the sticker price is $22,735, what is the dealer's markup rate?
change = vnew - vold = 22735 - 21636 = $1,099 markup
r = change/vold = 1099/21636 = 0.0507949713 ≈ 5.08% markup
Suppose the invoice price for a Chevy Malibu is $21,636 and the sticker price is $22,735. If the car dealer is willing to sell the car at 3.5% off the sticker price, what is the sale price and what is the dealer's markup?
change = rvold = 0.035 * 22735 ≈ $796 discount vnew = vold + change = 22735 - 796 = $21,939 sale price change = vnew - vold = 21939 - 21636 = $303 markup r = change/vold = 303/21636 = 0.014004437 ≈ 1.40% markup
The number of traffic fatalities in Kentucky in 2007 was 864. In 2008 the number of traffic fatalities went down 4.51% (compared to 2007) and in 2009, the number of traffic fatalities went down again (by 4.12% compared to 2008). How many traffic fatalities (rounded to the nearest integer) were there in 2008 and 2009? What was the percent change in traffic fatalities from 2007 to 2009?
change = rvold = 0.0451 * 864 ≈ 39 fewer fatalities in 2008 vnew = vold + change = 864 - 39 = 825 fatalities in 2008 change = rvold = 0.0412 * 825 ≈ 34 fewer fatalities in 2009 vnew = vold + change = 825 - 34 = 791 fatalities in 2009 change = vold - vnew = 864 - 791 = 73 fewer fatalities in 2009 than 2007 r = change/vold = 73/864 = 0.0844907407 ≈ 8.45% fewer fatalities
The number of traffic fatalities in Kentucky decreased by 8.45% from 2007 to 2009.
Kentucky has a 6% sales tax. However, food and some other things are not subject to this sales tax. Suppose a man goes on a Wal-Mart run and buys a variety of items. If his purchases added up to $143.87 and he was charged an additional $3.12 for sales tax, find the total cost of the taxable items he purchased and the total cost of the non-taxable items he purchased.
change = rvold (this represents the tax)
implies vold = change/r = 3.12/0.06 ≈ $56.00 worth of taxable items
143.87 - 56.00 = $87.87 worth of non-taxable items
A newsperson reports that last year's rainfall (a total of 45 inches) was 15% above average. What is the average annual rainfall?
vnew = vold + change = vold + rvold = vold(1 + r)
implies vold = vnew/(1 + r) = 45/1.15 ≈ 39.1 inches
The average annual rainfall is about 39.1 inches.