Chapter 2 Study Guide
Review:
Percent proportion:
is = %
of 100
Example: What percent of 50 is 40?
40 = x cross multiply
50 100
50x = 4000 divide by number in front of variable
50 50
X = 80%
Percent equation:
% ∙ of = is or % ∙ whole = part
Example: What percent of 50 is 40?
x∙50 = 40 rewrite correctly
50x = 40
50x = 40 divide both sides by number in front of variable
50 50
X = .8 change to percent
X = 80%
Percent of Change
%change = difference x 100
Original amount
Difference = difference between original and new (always positive)
It is either Increase (number increases) or Decrease(number decreases)
Example: A video game originally sold for $50. It is now selling for $36. What is the percent of change?
Original = $50
New = $36
Decrease
% change = 50 - 36 x 100 = 14 x 100 = 0.28 x 100 = 28%
50 50
Percent of Error
% error = difference between actual & estimate x 100
Actual amount
The difference between the actual and estimate is always positive
Example: Mrs. Moschetti has a jar of marbles. You guess that there are 50 marbles in the jar. The actual amount of marbles is 65. What is your percent of error?
Guess = 50
Actual = 65
% error= 65 - 50 x 100 = 15 x 100 = 0.23 x 100 = 23%
65 65
Mark-up (Add)
Mark-up = (% as a decimal)x(original amount)
Total = original amount + mark-up
Example: A sweater’s original price is $35. The store will markup the price up by 56%. What is the final selling price?
56% = .56
X = .56(35.00)
X = $19.60 (mark-up)
35.00 + 19.60 = $54.60 (selling price)
Discount (Subtract)
Discount = (% as a decimal)x(original amount)
Total = original amount - discount
Example: A sweater’s original price is $35. The sweater is on sale for 30%. What is the final selling price?
30% = .30
X = .30(35.00)
X =$10.50 (discount)
35.00 – 10.50 = $25.50 (sale price)
Tax (Add)
Tax = (% as a decimal)x(original amount or bill)
Total = original amount or bill + tax
Example: Bill buys a video game for $60. He has to include 7% tax. What is the final price?
7% = .07
X = .07(60.00)
x = $4.20 (tax)
60.00 + 4.20 = $64.20 (final price)
Tip (Add)
Tip = (% as a decimal)x(original bill)
Total = original bill + tip
Example: A family goes out to dinner. The bill is $90. The family wants to leave a 20% tip. What is their final bill?
20% = .20
X = .20(90.00)
x = $18.00 (tip)
90.00 + 18.00 = $108.00 (final bill)
Combo Problem Tax & Tip (Add, Add)
Tip = (% as a decimal) x (original bill)
Tax = (% as a decimal) x (original bill)
Total = original bill + tip + tax
Example: A family goes out to dinner. The bill is $90. The family wants to leave a 20% tip. They must include the 7% tax. What is their final bill?
20% = .20 7% = .07
X = .20(90.00) X = .07(90.00)
x = $18.00 (tip) x = $6.30 (tax)
90.00 + 18.00 + 6.30 = $114.30 (final bill)
Combo Problem Discount & Tax (Subtract, Add)
Discount = (% as a decimal) x (original amount)
Sale price = original amount - discount
Tax = (% as a decimal) x (Sale price)
Selling price = total + tax
Example: A bicycle’s original price is $185. The bicycle is on sale for 30%. You must pay 7% tax on the sale price. What is the final selling price?
30% = .30
X = .30(185.00)
X = $55.50 (discount)
185.00 – 55.50 = $129.50 (sale price)
7% = 0.07
x = .07(129.50)
x = $9.07
129.50 + 9.07 = $138.57 (selling price)
Commission (Add)
Commission = (% as a decimal) x (original pay)
Example:John is selling sets of knives and makes a 10% commission on all sales. What would his commission be on the sale of a $3250 set of knives?
X = .10(3250.00)
x = $325.00 Commission
Original Price
Subtract % from 100 and convert to decimal = % paid
Sale price = (% paid as a decimal) x (original price)
Divide by % paid (decimal) on both sides
Example:A sweater is on sale for $52. This price is 25% less than the original price. What is the original price?
100 – 25 = 75% = .75
52 = .75(x)
.75 .75
x = $69.33 (original price)
Simple Interest Formula: I = prt
I = Interest earned or paid
P = principal (clues: invested, deposited, loaned, borrowed, placed)
R = interest rate (always as a % convert to a decimal)
T = time in years (if less than a year place months over 12)
Example:John invests $1600 in a savings account. The account pays 3% simple interest. How much interest will he earn in 5 years? How much interest will he earn in 5 months?
P = $1600
R = 3% = 0.03
a)T = 5 years
I=PRt = (1600)(0.03) (5) = $240 (interest)
b)T = 5 months years
I=PRt = (1600)(0.03) () = $20 (interest)
Working Backwards (Find P, R or T):
Example:John invests $1600 in a savings account. He earns $240 interest over 5 years. What interest rate is the account paying?
I = $240
P = $1600
R = ?
T = 5 years
I=PRt
240 = (1600)R(5) 1600 x 5 = 8000
240 = 8000R Divide both sides by 8000
8000 8000
0.03 = R Move decimal 2 places to the right
3% = R Make %