1. Applications for Systems of Equations Algebra I

2. Example #1  Flying to Ankara with a tailwind a plane averaged 368 mph. On the return trip the plane only averaged 332 mph while flying back into the same wind. Find the speed of the plane in still air and the speed of the wind.  Solution: let x be the planes speed and y the winds speed x + y = 368 (With the wind) x – y = 332 (Against the wind)  Answer: Plane 350mph Wind 18mph

3. Example #2  Traveling with the current a certain boat went 19 mph. Against the same current the boat only went 3 mph. What’ s the speed of the current? What’s the speed of the boat in still water?  Solution: Let x = boats speed and y = currents speed x + y = 19(with current) x – y = 3(against current)  Answer: Boat 11mph, Current 8mph

4. Example #3  The difference of two numbers is 1 Their sum is 15. Find the numbers.  Solution: Let x and y be the numbers x – y = 1 x + y = 15  Answer: 7 and 8

5. Example #4  The sum of the digits of a certain two-digit number is 10. When you reverse the digits you increase the number by 54. What’s the number?  Solution: Let x be the tens digit and y be the ones digit. x + y = 10 (10y + x) – (10x + y) = 54 OR Use guess and check to find the solution.  Answer: 28

6. Example #5  A boat traveled 312 miles downstream and back. The trip down stream took 12 hours. The trip back took 39 hours. What is the speed of the boat in still water? What is the speed of the current?  Solution: Let x = boats speed and y = currents speed remember d=rt 12(x + y) = 312 39(x – y) = 312  Answer: Boat 17mph, Current 9mph

7. Example #6  New York City is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 9 vans and 14 buses with 739 students. High School B rented and filled 5 vans and 12 buses with 609 students. Every van had the same number of students as did the buses. Find the number of students in each van and in each bus.  Solution: Let x = students in vans and y = students in buses 9x + 14y = 739 5x + 12y = 609  Answer: 9 students per van and 47 per bus.

8. Example #7  Krystal’s school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 6 senior citizens tickets and 6 child tickets for a total of $138. the school took in $151 on the second day by selling 7 senior citizens tickets and 6 child tickets. Find the price of a senior ticket and the price of a child ticket.  Solution: Let x = price for a seniors ticket and y = price for a child’s ticket 6x + 6y = 138 7x + 6y = 151  Answer: $13 for a senior ticket and $10 for a child’s ticket