1. 2.2: Solving Equations Through Various Methods
Page 87 3) 3 7)
{≈–2.4265}
11)
{≈–1.4751, ≈1.2372}
15)
{≈–1.3794, ≈1.6030}
19)
{≈–2.1149, ≈0.2541, ≈1.8608}
23)
{≈–1.7521}
27)
{0, ≈2.2074}
31)
{≈–0.6514, ≈1.1513}
33)
{≈7.0334}
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2.2: Solving Equations Through Various Methods

2. Pre-Calculus AB Pre-AP/Dual, Revised ©2015
Applications
Section 2.3
Pre-Calculus AB Pre-AP/Dual, Revised ©2015
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2.3: Applications

3. Steps
Read the problem 2 times. Once to read it, a second time to note all critical information, and lastly to determine the equation needed and what is being asked for.
Determine the variables
Draw a picture if applicable.
Translate from English to Math.
Solve for at least one variable.
Find any remaining information.
Interpret your answer.
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2.3: Applications

4. Example 1
The average of two real numbers is One number is 1500 times the reciprocal of the other. Find the two numbers.
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2.3: Applications

5. Example 1
The average of two real numbers is One number is 1500 times the reciprocal of the other. Find the two numbers.
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2.3: Applications

6. Example 2
The sum of two numbers is 15 and the difference of the squares is 5. What are the numbers?
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2.3: Applications

7. Example 3
The width of a rectangle is three times its height. If it has an area of square feet, what are the dimensions?
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2.3: Applications

8. Your Turn
A rectangle is twice as wide as it is high. If it has an area of 24.5 in2, what are its dimensions? What are the numbers?
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2.3: Applications

9. Example 4
A real estate investment yields a return of 10% per year and a certificate of deposit (CD) which paus 6% per year. How much of $7,500 should be put in the real estate investment and how much should be put into the CD to obtain a return of 7% on the entire $7,500?
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2.3: Applications

10. Example 4
A real estate investment yields a return of 10% per year and a certificate of deposit (CD) which paus 6% per year. How much of $7,500 should be put in the real estate investment and how much should be put into the CD to obtain a return of 7% on the entire $7,500?
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2.3: Applications

11. Example 5
You have already invested $550 in a stock with an annual return of 11%. How much of an additional $1100 should be invested at 12% and how much at 6% so that the total return on the entire $1,650 is 9%?
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2.3: Applications

12. Example 5
You have already invested $550 in a stock with an annual return of 11%. How much of an additional $1100 should be invested at 12% and how much at 6% so that the total return on the entire $1,650 is 9%?
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2.3: Applications

13. Your Turn
A high risk stock pays dividends at a rate of 12% per year and a savings account which pays 6% interest per year. How much of the $9,000 investment should be put in the stock and how much should be put in savings to obtain a return of 8% per year on the total investment?
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2.3: Applications

14. Your Turn
A high risk stock pays dividends at a rate of 12% per year and a savings account which pays 6% interest per year. How much of the $9,000 investment should be put in the stock and how much should be put in savings to obtain a return of 8% per year on the total investment?
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2.3: Applications

15. Example 6
A chemist has 30 ml of a 40% acid solution in a test tube. How much of the solution should be poured off and replaced with pure acid so that the new mix is 70% acid?
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2.3: Applications

16. Example 7
A canoeist paddled a total of 11 hours on a 48 km round trip to Bear Lake. The upstream trip followed a period of heavy rain and the current he paddled against was 3 km/h. For the downstream return trip, he paddled with the current that slowed to 2 km/hr. At what speed would he paddle the canoe in still water?
Distance
Rate
Time
Downstream
Upstream
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2.3: Applications

17. Example 7
A canoeist paddled a total of 11 hours on a 48 km round trip to Bear Lake. The upstream trip followed a period of heavy rain and the current he paddled against was 3 km/h. For the downstream return trip, he paddled with the current that slowed to 2 km/hr. At what speed would he paddle the canoe in still water?
Distance
Rate
Time
Downstream
Upstream
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2.3: Applications

18. Example 7
A canoeist paddled a total of 11 hours on a 48km round trip to Bear Lake. The upstream trip followed a period of heavy rain and the current he paddled against was 3 km/h. For the downstream return trip, he paddled with the current that slowed to 2 km/hr. At what speed would he paddle the canoe in still water?
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2.3: Applications

19. Austin to Colorado Springs Colorado Springs to Austin
Your Turn
A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown?
Distance
Rate
Time
Austin to Colorado Springs
Colorado Springs to Austin
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2.3: Applications

20. Austin to Colorado Springs Colorado Springs to Austin
Your Turn
A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown?
Distance
Rate
Time
Austin to Colorado Springs
Colorado Springs to Austin
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2.3: Applications

21. Your Turn
A pilot wants to make an 840-mile road trip from Austin to Colorado Springs and back in 5 hours flying time. There will be a headwind of 30 mph going to Colorado Springs, and it is estimated that there will be 40-mph tailwind returning to Austin. At what constant engine speed should the plane be flown?
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2.3: Applications

22. Assignment
Worksheet
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2.3: Applications