Solve Percent Problems by Direct Translation. Type 1: What number is 8% of 215?

Transcription

1 Solve Percent Problems by Direct Translation Type 1: What number is 8% of 215? In the question What number is 8% of 215?, the words what number represent the amount, 8% represents the percent, and 215 represents the base. In these problems, the word is means is equal to, and the word of means multiplication. Type 2: 102 is 21.3% of what number? Type 3: 31 is what percent of 500?

2 EXAMPLE By the year 2050, a study by the Pew Research Center predicts that about 81 million residents of the U.S. will be age 65 or older. The circle graph (or pie chart) indicates that age group will make up 18.5% of the population. If this prediction is correct, what will the population of the United States be in 2050? (Round to the nearest million.)

3 EXAMPLE: The Federal Trade Commission receives complaints involving the theft of someone s identity information, such as a credit card, Social Security number, or cell phone account. Refer to the data in the table. What was the percent of increase in the number of complaints from 2008 to 2009? (Round to the nearest percent.)

4 FORMULAE Retail Price = Cost + Markup Profit = Revenue Cost Simple Interest = Principal * rate of interest *time Speed = Distance Time Perimeter of 2 dimensional figure: Square = 4*length Rectangle = 2 * (l+w) Circle = 2πr Triangle = a + b + c (a, b, c are lengths of the sides of a triangle)

5 Estimates are that Warner Brothers made a $219 million profit on the film Harry Potter and the Half-Blood Prince. If the studio received $469 million in worldwide box office revenue,find the cost to make and distribute the film. As they migrate from the Bering Sea to Baja California, gray whales swim for about 20 hours each day, covering a distance of approximately 70 miles. Estimate their average swimming rate in miles per hour. (Source: marinebio.net) The largest flag ever flown was an American flag that had a perimeter of 1,520 feet and a length of 505 feet. It was hoisted on cables across Hoover Dam to celebrate the 1996 Olympic Torch Relay. Find the width of the flag. 2.5 More on problem solving The first part of California s magnificent 17-Mile Drive begins at the Pacific Grove entrance and continues to Seal Rock. It is 1 mile longer than the second part of the drive, which extends from Seal Rock to the Lone Cypress. The final part of the tour winds through the Monterey Peninsula, eventually returning to the entrance. This part of the drive is 1 mile longer than four times the length of the second part. How long is each part of 17-Mile Drive Solve consecutive number problems: The year George Washington was chosen president and the year the Bill of Rights went into effect are consecutive odd integers whose sum is 3,580. Find the years

6 Solve Geometry Problems: Police used 400 feet of yellow tape to fence off a rectangular-shaped lot for an investigation. Fifty less feet of tape was used for each width as for each length. Find the dimensions of the lot Simple interest problems: A college student invested the $12,000 inheritance he received and decided to use the annual interest earned to pay his tuition cost of $945. The highest rate offered by a bank at that time was 6% annual simple interest. At this rate, he could not earn the needed $945, so he invested some of the money in a riskier, but more profitable, investment offering a 9% return. How much did he invest at each rate? Solve Uniform Motion: A cargo ship, heading into port, radios the Coast Guard that it is experiencing engine trouble and that its speed has dropped to 3 knots (this is 3 sea miles per hour). Immediately, a Coast Guard cutter leaves port and speeds at a rate of 25 knots directly toward the disabled ship, which is 56 sea miles away. How long will it take the Coast Guard to reach the ship? Mixing Solutions: A chemistry experiment calls for a 30% sulfuric acid solution. If the lab supply room has only 50% and 20% sulfuric acid solutions, how much of each should be mixed to obtain 12 liters of a 30% acid solution? Dry Mixtures: Because cashews priced at $9 per pound were not selling, a produce clerk decided to combine them with less expensive peanuts and sell the mixture for $7 per pound. How many pounds of peanuts, selling at $6 per pound, should be mixed with 50 pounds of cashews to obtain such a mixture? A restaurant owner needs to purchase some tables, chairs, and dinner plates for the dining area of her establishment. She plans to buy four chairs and four plates for each new table. She also plans to buy

7 20 additional plates in case of breakage. If a table costs $100, a chair $50, and a plate $5, how many of each can she buy if she takes out a loan for $6,500 to pay for the new items?