Post on 12-Jan-2016
transcript
OTCQ
What is 10% of 200?
Aim 3 -7 How do we define and handle
percents?
NY AN 5
Percents
7% commission rate.
For every $100 of sales, you will earn $7.
100
7
Percents
5.5% tax rate.
For every $100 of merchandise that you buy, you will pay $5.50 in sales tax.
100
5.5
Percents – Conversion to other Forms
65%100
6565.0
Percents – Conversion to other Forms
4%100
404.0
Rule - % to Decimal
To convert a percent to a decimal:1. Remove the % symbol
2. Move the decimal point two positions to the left.
72%.
Practice - % to Decimal
13%
2%
120%
= .13
= .02
= 1.20
Practice - % to Decimal One More!!!
%4
3%75.0
0075.0
Rule – Decimal to %
To convert a decimal to a percent:1. Move the decimal point two positions to the right.
2. Add the % symbol
0 38. %
Practice – Decimal to %
0.55
0.004
2
= 55%
= 0.4%
= 200%
The Components of a Percent Problem
Components B, P, R
Base
Part
Rate
In the Administrative Assistant Program at SWTC there are 18 students. 12 of them, or about 67%, reside in Grant County.
Components B, P, R
Base
Part
Rate
Dave is a salesperson paid on a commission rate of 7%. Last week his weekly sales were $21,500, so he earned $1,505.
Components B, P, R
Base
Part
Rate
45 is 90% of 50.Rate BasePart
Solving Percent Problems
Percent Formulas Part = Base x Rate
P = B x R
Base = Part Rate B = P R
Rate = Part Base R = P B
P
B R
20% of the cars in the upper parking lot are blue. If there 135 cars in the lot, how many are blue?
Solve Percent ProblemsP
B R
Part = ____
Part = Base x Rate
Part = 135 x 20%
Part = 135 x 0.20
Part = 27
A person took the written portion of her driver’s test. She got 30 out of 35 correct. What is her score expressed as a percent?
Solve Percent ProblemsP
B R
Rate = ____
Rate = Part Base
Rate = 30 35
Rate = 0.85714
Rate = 85.7%
On a day when it snowed heavily, 33 people, which is 55% of a company’s total workforce made it to work on-time. What is the size of the company’s workforce?
Solve Percent ProblemsP
B R
Base = ____
Base = Part Rate
Base = 33 55%
Base = 33 0.55
Base = 60
Solve Generic Percent Problems
18% of what number is 900?
Solve Percent ProblemsP
B RBase = ____
Base = Part Rate
Base = 900 18%
Base = 900 0.18
Base = 5000
What percent of 40 is 30?
Solve Percent ProblemsP
B RRate = ____
Rate = Part Base
Rate = 30 40
Rate = 0.75
Rate = 75%
22% of 650 is what number?
Solve Percent ProblemsP
B RPart = ____
Part = Base x Rate
Part = 650 x 22%
Part = 650 x 0.22
Part = 143
Solving Percent of Increase Problems
Steps to solve percent of increase problems.
Method #1: To find % increase.
Confirm an increase from the base in one period to a new base in another period.
Step 1:
Subtract new base – base = part
Step 2: Solve BR = P
Method #1: To find % increase.
Confirm an increase from the base in one period to a new base in another period.
Step 1:Subtract new base – base = part
Step 2: Solve BR = P
Example:Assume that you had 150 cats in your town at the start of this year. In a new count you found 225 cats. What is the percent of increase?
Method #1: To find % increase.
Confirm an increase from the base in one period to a new base in another period.
Step 1: Subtract
new base – base = part
Step 2: Solve BR = P
Example:Assume that you had 150 cats in your town at the start of this year. In a new count you found 225 cats. What is the percent of increase?
225 – 150 = 75
150(R) = 75R = .50 50%
Method #1: To find % increase.
Confirm an increase from the base in one period to a new base in another period.
Step 1:Subtract new base – base = part
Step 2: Solve BR = P
Example:Assume that you had 650 cars in your parking lot yesterday. Today you counted 800. What is the percent of increase? 800 – 650 = 150
650(R) = 150R= 150/650 = 3/13= .2323%
Steps to solve percent of decrease problems.
Method #1: To find % decrease.
Confirm a decrease from the base in one period to a new base in another period.
Step 1:
Subtract base – new base = part
Step 2: Solve BR = P
Method #1: To find % decrease.
Confirm a decrease from the base in one period to a new base in another period.
Step 1:Subtract base – new base = part
Step 2: Solve BR = P
Example:Assume that you had 150 cats in your town at the start of this year. In a new count you found 50 cats. What is the percent of decrease?
Method #1: To find % decrease.
Confirm a decrease from the base in one period to a new base in another period.
Step 1:Subtract base – new base = part
Step 2: Solve BR = P
Example:Assume that you had 150 cats in your town at the start of this year. In a new count you found 50 cats. What is the percent of decrease?
150 – 50 = 100
BR = P 150(R) = 100R = 10/15 = .66 = 66%
Method #1: To find % decrease.
Confirm a decrease from the base in one period to a new base in another period.
Step 1:Subtract base – new base = part
Step 2: Solve BR = P
Example:Assume that you had 550 cars in your parking lot on Sunday. On Monday, you counted 350 cars. What is the percent of decrease?
Method #1: To find % decrease.
Confirm a decrease from the base in one period to a new base in another period.
Step 1:Subtract base – new base = part
Step 2: Solve BR = P
Example:Assume that you had 550 cars in your parking lot on Sunday. On Monday, you counted 350 cars. What is the percent of decrease?
550 – 350 = 200
Method #1: To find % decrease.
Confirm a decrease from the base in one period to a new base in another period.
Step 1:Subtract base – new base = part
Step 2: Solve BR = P
Example:Assume that you had 550 cars in your parking lot on Sunday. On Monday, you counted 350 cars. What is the percent of decrease?
550 – 350 = 200550(R) = 200
Method #1: To find % decrease.
Confirm a decrease from the base in one period to a new base in another period.
Step 1:Subtract base – new base = part
Step 2: Solve BR = P
Example:Assume that you had 550 cars in your parking lot on Sunday. On Monday, you counted 350 cars. What is the percent of decrease?
550 – 350 = 200550(R) = 200 __R = 200/550 = 0.3636Approximately 36%
Percent Increase/Percent Decrease from another perspective.
Your new car has 305 horsepower. Your new car has 25% more horsepower than your old car.
How many horsepower does your old car have?
old car = Base 305 hp = part.
25% more means 125%.
BR = PBase (1.25) = 305
B = 305/1.25B = 244
Solution Method Increase
Old car = ______ hp New car = 305 hp This is a 25% increase in hp.
Original Value + Increase = New Value
Base Part
100%
??? 305
25% 125%
R
PB
1.00 (base) + .25(base)= 305hint: combine like terms.Start HWK in Glencoe
1.00 (base) + .25(base)= 305combine like terms 1.25(base)= 305divide by 1.25base = 244
Your business had $48,000 in revenue this year. Your business had 5% more revenue this year in comparison to last year. What was the revenue of your business last year?
Solution Method Increase
Last Year’s Revenue = ______ This Year’s Revenue = $48,500 This is a 5% increase in earnings.
Original Value + Increase = New Value
Base Part
100%
??? $48,500
5% 105%
R
PB
1.00(base) + .05(base)= $48,000combine like terms 1.05(base)= $48,000divide by 1.05base = $45,714.29
Solving Decrease Problems
Sample Problems
Hometown Restaurant had sales of $12,800 this month. This is a 35% drop in sales compared to the same time last year. Determine the restaurant’s sales at this time last year?
Solution Method Decrease
Sales This Month = $12,800 Sales for this month 1 year ago = ______ This is a 35% drop in sales
Original Value - Decrease = New Value
Base Part
100%
??? $12,800
35% 65%
R
PB
1.00(base) - .35(base)= $12,800combine like terms .65(base)= $12,800divide by .65base = $19,692.31check multiply .65 (19,692.31)
Sample Problem
Sara Lee Company had $230 million this quarter in revenues, which is a 25% decrease from the last quarter. What were the company’s earnings last quarter?
Solution Method Decrease
Earnings This Quarter = $230 million Earning Last Quarter = ______ This is a 25% drop in sales
Original Value - Decrease = New Value
Base Part
100%
??? $230 million
25% 75%
R
PB
1.00(base) -.25(base)=$230,000,000combine like terms .75(base)= $230,000,000divide by .75base = $306666666.67check multiply .75 ($306666666.67)
Percent Change
Percent Change 1 of 3
Example: Two weeks ago, the price of gas was about $2.92/gallon. Today it is $3.07/gallon. What is the percent increase in the price of gas?
Rate = ?
Part = _________________Amount of Increase
Base = _________________Original Price
$3.07 – $2.92$0.15
$2.92
Last week a business had 447 paying customers. This week they had 521. What is the percent increase in the number of paying customers?
Percent Change 2 of 3
Rate = ?
Part = _________________Amount of Increase
Base = _________________Original Amount
521 – 44774
447
Last year 235 registered voters participated in the local election. This year, 210 did. What is the percent decrease in the number of voters?
Percent Change 3 of 3
Rate = ?
Part = _________________Amount of Decrease
Base = _________________Original Amount
235 – 21025
235
Percent Change One More!
Last week Jim mowed 16 yards. This week he mowed 6 more than the previous week. What is the percent increase in the number of yards he mowed?
Rate = ?
Part = _________________Amount of Increase
Base = _________________Original Amount
6
16
Challenge Problems
Restaurant charges 8% sales tax on all orders. Total sales for a day are $1026 including tax. a) What were the sales w/out tax? b) Find the amount that is sales tax.
Sales + Tax = Grand Total
Sales = $950
Tax = $76
WallPaper Plus: This store offers a 20% discount to students. This store charges a sales tax of 7%.If you buy $150 dollars worth of wallpaper, prove which choice leads to a lower total cost:t
1. Apply the 20% discount to the $150 and then add 7% tax; or
2. Apply the 7% tax to the $150 and then apply the 20% discount to the total with tax.
1. Apply the 20% discount to the $150 and then add 7% tax;
To apply the 20% discount, use BR=P
$150 (.20) = $30 discount
Discounted price = $150 - $30 = $120
Sales tax: use BR=P
$120(.07) = $8.40
Total with tax = $120 + $8.40 = $128.40
2.Apply the 7% tax to the $150 and then apply the 20% discount to the total with tax.
Sales tax: use BR=P
$150(.07) = $10.50
Total with tax = $150 + $10.50 = $160.50
To apply the 20% discount, use BR=P
$160.50 (.20) = $32.10 discount
Discounted price = $160.50 - $32.10 = $128.40
SAME TOTAL COST EITHER WAY!!!!!!!
Three day auction; Day 1 $5750 in sales, Day 2 $4186 in sales, with 28% of the original equipment remaining to be sold on Day 3. Determine the value of the remaining equipment.
Original Amt. of Equip – Amt. Sold = Amt. Remaining
Original Amt. of Equip = $13,800
Amt. Remaining = $3864
Student spent $3450 for tuition and $4350 for dorm fees. 35% of his original savings are left.
Determine the amount of savings he still has left.
Original Amt. of Money – Amt. Spent = Amt. Left
Orig. Amt of $ = $12,000
Amt. Left = $4,200