Population, Heart Rate, and Math Equations for Real-Life Problems

1. decrease in population original population current population minus is Example 4: Application Over 20 years, the population of a town decreased by 275 people to a population of 850. Write and solve an equation to find the original population. p– d = c Write an equation to represent the relationship. p – d = c p – 275 = 850 Since 275 is subtracted from p, add 275 to both sides to undo the subtraction. + 275+ 275 p =1125 The original population was 1125 people.

2. Check It Out! Example 4 A person's maximum heart rate is the highest rate, in beats per minute, that the person's heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find a person's age if the person's maximum heart rate is 185 beats per minute.

3. added to maximum heart rate 220 age is Check It Out! Example 4 Continued a+ r = 220 a + r = 220 Write an equation to represent the relationship. a + 185 = 220 Substitute 185 for r. Since 185 is added to a, subtract 185 from both sides to undo the addition. – 185– 185 a = 35 A person whose maximum heart rate is 185 beats per minute would be 35 years old.

4. 1 Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year. 4 Example 4: Application one-fourth times earnings equals college fund Write an equation to represent the relationship. Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. Ciro earned $1140 mowing lawns. m = $1140

5. Check it Out! Example 4 The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began. Distance divided by 3 equals height in thousands of feet Write an equation to represent the relationship. Substitute 45 for d. 15 = h The plane was flying at 15,000 ft when the descent began.

6. 7. A person's weight on Venus is about his or her weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus. 9 10 Lesson Quiz: Part 2

7. Example 4: Application Jan joined the dining club at the local café for a fee of $29.95. Being a member entitles her to save $2.50 every time she buys lunch. So far, Jan calculates that she has saved a total of $12.55 by joining the club. Write and solve an equation to find how many time Jan has eaten lunch at the café.

8. 1 Understand the Problem Example 4: Application Continued The answer will be the number of times Jan has eaten lunch at the café. List the important information: • Jan paid a $29.95 dining club fee. • Jan saves $2.50 on every lunch meal. • After one year, Jan has saved $12.55.

9. Make a Plan amount saved on each meal total amount saved dining club fee = – 2 Example 4: Application Continued Let m represent the number of meals that Jan has paid for at the café. That means that Jan has saved $2.50m. However, Jan must also add the amount she spent to join the dining club. 12.55 = 2.50m – 29.95

10. 3 Solve + 29.95 + 29.95 42.50 = 2.50m 2.50 2.50 Example 4: Application Continued Since 29.95 is subtracted from 2.50m, add 29.95 to both sides to undo the subtraction. 12.55 = 2.50m – 29.95 42.50 = 2.50m Since m is multiplied by 2.50, divide both sides by 2.50 to undo the multiplication. 17 = m

11. 4 Look Back Example 4: Application Continued Check that the answer is reasonable. Jan saves $2.50 every time she buys lunch, so if she has lunch 17 times at the café, the amount saved is 17(2.50) = 42.50. Subtract the cost of the dining club fee, which is about $30. So the total saved is about $12.50, which is close to the amount given in the problem, $12.55.

12. Check It Out! Example 4 Sara paid $15.95 to become a member at a gym. She then paid a monthly membership fee. Her total cost for 12 months was $735.95. How much was the monthly fee?

13. 1 Understand the Problem Check It Out! Example 4Continued The answer will the monthly membership fee. List the important information: • Sara paid $15.95 to become a gym member. • Sara pays a monthly membership fee. • Her total cost for 12 months was $735.95.

14. Make a Plan monthly fee total cost initial membership + = 2 Check It Out! Example 4Continued Let m represent the monthly membership fee that Sara must pay. That means that Sara must pay 12m. However, Sara must also add the amount she spent to become a gym member. 735.95 = 12m + 15.95

15. 3 Solve – 15.95 – 15.95 720 = 12m 12 12 Check It Out! Example 4Continued Since 15.95 is added to 12m, subtract 15.95 from both sides to undo the addition. 735.95 = 12m + 15.95 720 = 12m Since m is multiplied by 12, divide both sides by 12 to undo the multiplication. 60 = m

16. 4 Look Back Check It Out! Example 4Continued Check that the answer is reasonable. Sara pays $60 a month, so after 12 months Sara has paid 12(60) = 720. Add the cost of the initial membership fee, which is about $16. So the total paid is about $736, which is close to the amount given in the problem, $735.95.

17. Example 11: Application Jon and Sara are planting tulip bulbs. Jon has planted 60 bulbs and is planting at a rate of 44 bulbs per hour. Sara has planted 96 bulbs and is planting at a rate of 32 bulbs per hour. In how many hours will Jon and Sara have planted the same number of bulbs? How many bulbs will that be?

18. 32 bulbs each hour 44 bulbs each hour the same as 60 bulbs 96 bulbs ? When is plus plus Example 11: Application Continued Let b represent bulbs, and write expressions for the number of bulbs planted. 60 + 44b = 96 + 32b 60 + 44b = 96 + 32b To collect the variable terms on one side, subtract 32b from both sides. – 32b– 32b 60 + 12b = 96

19. Example 11: Application Continued 60 + 12b = 96 Since 60 is added to 12b, subtract 60 from both sides. –60 – 60 12b = 36 Since b is multiplied by 12, divide both sides by 12 to undo the multiplication. b = 3

20. Example 11: Application Continued After 3 hours, Jon and Sara will have planted the same number of bulbs. To find how many bulbs they will have planted in 3 hours, evaluate either expression for b = 3: 60 + 44b = 60 + 44(3) = 60 + 132 = 192 96 + 32b = 96 + 32(3) = 96 + 96 = 192 After 3 hours, Jon and Sara will each have planted 192 bulbs.

21. 7 . Example 12 Four times Greg's age, decreased by 3 is equal to 3 times Greg's age increased by 7. How old is Greg? Let g represent Greg's age, and write expressions for his age. three times Greg's age four times Greg's age is equal to increased by decreased by 3 4g – 3 = 3g + 7

22. –3g –3g + 3+ 3 Example 12Continued 4g – 3 = 3g + 7 To collect the variable terms on one side, subtract 3g from both sides. g – 3= 7 Since 3 is subtracted from g, add 3 to both sides. g = 10 Greg is 10 years old.