COURSE MODULE NAME PERCENTAGES

5.The price of an item decreased by 20% to $200. Then later the price decreased again from
$200 to $150. What is the percent of decrease from the original price to the final price of $150?
Solution to Problem 5:
We first need to find the original price x. The first decrease gives
x - 20% x = 200
0.8 x = 200
x = 200 / 0.8 = 250
The percentage decrease fro the original price 250 to 150 is given by
part / whole = (250 - 150) / 250 = 0.4 = 40%
6.A number increases from 30 to 40 and then decreases from 40 to 30. Compare the percent of
increase from 30 to 40 and that of the decrease from 40 to 30.
Solution to Problem 6:
Percent increase from 30 to 40 is given by
(40 - 30) / 30 = 10 / 30 = 0.33 = 33% (2 significant digits)
Percent decrease from 40 to 30 is given by
(40 - 30) / 40 = 0.25 = 25%
In absolute term, the percent decrease is less than the percent increase.
7.A family had dinner in a restaurant and paid $30 for food. They also had to pay 9.5% sale tax
and 10% for the tip. How much did they pay for the dinner?
Solution to Problem 7:
They paid for food, sales tax and tip, hence
total paid = $30 + 9.5% * 30 + 10% * 30 = $35.85
8.A shop is offering discounts on shirts costing $20 each. If someone buys 2 shirts, he will be
offered a discount of 15% on the first shirt and another 10% discount on the reduced price for the
second shirt. How much would one pay for two shirts at this shop?
Solution to Problem 8:
The reduced price for the first shirt
20 - 15% * 20 = $17
The reduced price for the second shirt. The 10% discount will be on the already
reduced price, hence the price of the second shirt is given by
17 - 10% * 17 = $15.3 The total cost for the two shirts is
17 + 15.3 = $32.3
9.Smith invested $5000 for two years. For the first year, the rate of interest was 7% and the
second year it was 8.5%. How much interest did he earn at the end of the two year period?
Solution to Problem 9:
Interest at the end of the first year
7% * 5000 = $350
Interest at the end of the second year
8.5% * (5000 + 350) = $454.75
Total interest at the end of the two year period is
$350 + $454.75 = $804.75
10.Janette invested $2000 at 5% compounded annually for 5 years. How much interest did she
earn at the end of the 5 year period?
Solution to Problem 10:
At the of the first year, she has the principal plus the interest on the principal
P1 = 2000 + 5% * 2000 = 2000(1 + 5%)
Percentages
12