1. Problem Solving Godwin Middle School Mr. Kozar

2.  Students will  Solve practical problems involving rational numbers, percents, ratios, and proportions.  Determine the percent increase or decrease for a given situation.

3. Vocabulary Vocabulary WordAssociated WordsDefinitionExample/Picture Amount of Discount Discount Price Discount Rate Formula Interest Mark-up Percent Percent of Change Principal Proportion Rate (interest, tax, unit) Sales Tax Simple Interest Tip

4.  Uses division to compare two numbers.  You can write ratios in 3 different ways……. abab a : ba to b

5.  Example:  A ski resort has 15 easy, 25 intermediate, 7 difficult, and 11 expert only trails. Write the ratio “intermediate trails : easy trails” in 3 ways. Intermediate trails = 25 = 5 easy trails 15 3 Answer: 5/3, 5: 3, 5 to 3

6.  A ratio that compares two quantities measured in different units.  Example: Lightning strikes about 100 times per second around the world. About how many times does lightning strike per minute around the world?  Solution: 60 sec = 1 min, 60 sec 100 times = 100 times x 60 sec 1 sec 1 sec 1min

7.  A rate that has a denominator of 1 unit.  Example: ▪ Write -24 feet per 5 seconds as a unit rate.  Solution: -24 ft = -24 ÷ 5 Simplify: - 24 ÷ 5 5 sec 5 ÷ 5 The unit rate is -4.8 ft per sec

8. Write ratios in 3 ways: (use numbers from example) Expert-only trails: easy trails Easy trails: difficult trails Write rate as a unit rate: 114 points 365 people 329 miles 6 games 5 months 10 gallons

9.  Is the percent off of an item.  Ex: A sales ad reads 20% off all merchandise.  Amount of discount = 20%  Sales Price (discount price)= the result from subtracting the discount from original price.

10.  Examples:  While shopping at a store, Billy found a $900 TV that was on sale at a discount rate of 30%. What is the sales price?  Solution: $900 x.30 = $270  Discount price: $900 - $270 = $630

11.  Original Price: $60 Percent Discount: 15% New Price:  Original Price: $42 Percent Discount: 30% New Price:  Original Price: $129 Percent Discount: 45%New Price:

12.  Percentage of tax applied to the sale of an item. Virginia State Tax rate is 5%.  Sales Tax is added to the price of the item.  Example: Big Mac Meal $4.49 + Tax (5%) Solution: $4.49 x.05 =.2245 roughly 23¢ So…. $4.49 +.23 = $4.72

13.  Small sum of money given as acknowledgement for services. (gratuity)  Example: Your restaurant bill is $25.89 w/tax.  Tipping norm is 10%-20%.  I choose 15% as my tip of the total bill.  Solution: $25.89 x.15 = $3.88  Total Bill = $25.89 + $3.88 = $29.77

14. Food Bill: $28.50 Tip: 18% Sales Tax: 4.5% Original Price: $58.40 Sales Tax: 5.5%

15.  Is a special ratio with a denominator of 100.  Examples: Sales Tax Rate (5% in VA) Tip Amount (10-15%)

16.  A price increase. Difference between the cost of the product and its price.  Example: A shirt has a wholesale price of $16. The percentage markup is 120%/ What is the retail price? 120% of $16. 1.2 x 16 = $19.20 $19.20 + $16 = $35.20

17.  Wholesale price: $64 Percent markup: 85%  Wholesale price: $60 Percent markup: 130%  Wholesale price: $35 Percent markup: 110%

18.  Old price: $32 New Price: $24  Old price: $19 New Price: $33.25  Old price: 199.99 New Price: 119.99 M=P2-P1 Mp=M divided by P1 M=markup amount P1=original price P2=markup price Mp=markup percentage Formula: OP-NP OP Formula: OP-NP OP

19.  Formula: amount of change ( new – original) original Example: Price of XBOX 360 in September 2011= $249.99 Price of XBOX 360 in September 2011= $199.99

20.  Amount of money paid for the use of money.  Interest rate- % of the invested or borrowed amount.  Simple Interest for a number of years is determined by multiplying the principal (loan amount) by the rate of interest by the number of years of the loan or investment. I = prt

21.  You deposit $500 in a savings account that pays simple interest rate of 2.5% per year. How much interest will you earn after 18 months? Interest = Principal x Rate x Time  Solution: Formula is I = prt (500) (0.025) (1.5) = 18.75

22.  Change the percent to decimal form. 5%-.25- 18%-.96- 130%-.87- 74%-1.4-

23.  I = $12.50 P = $500 R= T= 6 months  I = $89.25 P = $850 R= 5.25% T=  I = $260 P = R= 6.5% T= 4 years  I = $320 P = R= 8% T= 2 years

24.  An equation stating that two ratios are equal. a = c * b and d can NEVER = 0 b d Example: An adult rhino beetle weighs only 0.525 ounce but can carry about 446.25 ounces on its back. If a person were proportionately as strong as a rhino beetle, how much weight could a 100 pound person carry?

25. An adult rhino beetle weighs only 0.525 ounce but can carry about 446.25 ounces on its back. If a person were proportionately as strong as a rhino beetle, how much weight could a 100 pound person carry?  Hint: Cross Multiply then solve  446.25 = x 44,625 =0.525x 0.525 100 0.525 0.525 x= 85,000 lbs BeetlePerson Carries446.25 ozX lb Weighs0.525 oz100 lb

26. 6 = 3 C 4 N = 63 14 84 16.2 = x 67.4 134.8 8 = 0.4 A 0.62 B = 49.6 1.8 14.4 2.1 = 27.3 0.9 y