8.4 Guided Notes Names: ___________________ Applications of Systems Day 1 – Setting up Systems of Equations

I have 12 coins, a combination of nickels and dimes. The total value of the coins is 85 cents. I have how many of each coin? I bought 3 candy bars and 2 bags of chips and spent $5.40. My friend bought 2 candy bars and 5 bags of chip and spent $9.10. How much did each item cost? The perimeter of a rectangle is 24 feet, and the length is 3 times the width. What are the dimensions. Dan invested a total of $12,00. He invested some money at 3% and some at 5%, after a year he had earned a total of $460. How much did he invest at each rate?

Geometry Application:

The perimeter of a rectangle is 38 m. If the width were doubled and the length were increased by 19 m, the perimeter would be 88 m. What are the length and width of the original rectangle?

                 

Day 2 - Distance, Rate, and Time

Distance Formula or the uniform rate formula d =

Solve for Rate r =

Solve for Time t =

Distance, Rate, and Time Problems

       

     Wind and Current Applications: Into a headwind, the plane flew 2000 miles in 5 hours. With a tailwind, the return trip took 4 hours. Find the speed of the plane in still air and the speed of the wind.                                  

Day  1  -­‐  Problem  Set    Applications. Underline key concepts and focus on the last sentence. Remember to LABEL, LABEL, LABEL!

1. Willy Wonka sold 28 boxes of candy for a total of $2,220. Scrumdiddlyumptious chocolate bars cost $70 per box. Everlasting Gobstoppers cost $90 per box. How many of each box were sold?

A) Let Statements:

B) System:

C) Answer:

2. At Rita’s, ice cream cones cost $.90 and sundaes cost $1.65. One day, the receipts for a total of 148 cones and sundaes were $180.45. How many cones were sold?

! A) Let Statements:

B) System:

C) Answer:

3. Mr. Curran loves Ooka and places two orders, one at lunch and one at dinner. At lunch, Mr. Curran’s order was for 7 rolls of sushi and 2 cups of miso soup for $85. At dinner, his order was for 19 rolls of sushi and 6 cups of miso for $233. What are the individual prices for a sushi roll and a cup of miso soup? !

A) Let Statements:

B) System:

C) Answer:

D) How much would it cost if he ordered 9 rolls of sushi and 3 cups of miso soup? !

4. The width of a rectangle is 1 meter less than three times its length. If its perimeter is 62 meters, find the area of the rectangle. !

! A) Let Statements:

B) System:

C) Answer:

5. A collection of nickels and dimes is worth $3.30. There are 42 coins in all. How many of each type of coin are there? !

!A) Let Statements:

B) System:

C) Answer:

6. The sum of two numbers is negative nine. Their difference is one. What are the numbers? !

! A) Let Statements:

B) System:

C) Answer:

7. The length of a rectangle is 5 feet more than the width. The perimeter of the rectangle is 58 feet. Find the width of the rectangle. !

! A) Let Statements:

B) System:

C) Answer:

8. Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. For what number of shirts would the cost be the same?

! A) Let Statements:

B) System:

C) Answer:

D) Which company should you order from if you only want to buy 6 shirts?

How about 35 shirts? Explain.

   

Day  2  -­‐  Problem  Set    Distance, Rate, Time Problems

1. Two joggers start from opposite ends of an 8 mile course running towards each other. One jogger is running at a rate of 4 mph, and the other is running at a rate of 6 mph. After how long will the joggers meet?

Picture

2. Bob and Fred start from the same point and walk in opposite directions. Bob walks 2 miles per hour faster than Fred. After 3 hours they are 30 miles apart. How fast did each walk?

Picture

3. Two campers left their campsite by canoe and paddled downstream at an average speed of 12 mph. They turned around and paddled back upstream at an average rate of 4 mph. The total trip took 60 minutes. After how much time did the campers turn around downstream?

Picture

4. Mike leaves his house traveling 2 miles per hour. Joy leaves 6 hours later to catch up with him traveling 8 miles per hour. How long will it take her to catch up with him?

Picture

5. On a 130 mile trip a car traveled at an average speed of 55 mph and then reduced its speed to 40 mph for the remainder of the trip. The trip took 2.5 hours. For how long did the car travel 40 mph?

Picture

Distance, Rate, Time Problems (Setup the table yourself)

6. A passenger and a freight train start toward each other at the same time from two points 300 miles apart. If the rate of the passenger train exceeds the rate of the freight train by 15 miles per hour, and they meet after 4 hours, what must the rate of each be?

7. Two automobiles started at the same time from a point, but traveled in opposite directions. Their rates were 25 and 35 miles per hour respectively. After how many hours were they 180 miles apart?

8. A boy rides away from home in an automobile at the rate of 28 miles an hour and walks back at the rate of 4 miles an hour. The round trip requires 2 hours. How far does he ride?

9. A motorboat leaves a harbor and travels at an average speed of 8 mph toward a small island. Two hours later a cabin cruiser leaves the same harbor and travels at an average speed of 16 mph toward the same island. In how many hours after the cabin cruiser leaves will the cabin cruiser be alongside the motorboat?

10. A jet plane traveling at 600 mph overtakes a propeller-driven plane, which has had a 2 hour head start. The propeller-driven plane is traveling at 200 mph. How far from the starting point does the jet overtake the propeller-driven plane?

11. A car traveling at 48 mph overtakes a cyclist who, riding at 12 mph, has had a 3 hour head start. How far from the starting point does the car overtake the cyclist?

12. A bus traveling at a rate of 60 mph overtakes a car traveling at a rate of 45 mph. If the car had a 1 hour head start, how far from the starting point does the bus overtake the car? !

13. On a 130 mi trip, a car traveled at an average speed of 55 mph and then reduced its speed to 40 mph for the remainder of the trip. The trip took a total of 2.5 h. For how long did the car travel at 40 mph?

14. An executive drove from home at an average speed of 40 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at and average speed of 60 mph. The entire distance was 150 mi. The entire trip took 3 h. Find the distance from the airport to the corporate offices.

15. A truck leaves a depot at 11 A.M. and travels at a speed of 45 mph. At noon, a van leaves the same place and travels the same route at a speed of 65 mph. !At what time does the van overtake the truck? !

16. Ariella drove 40 miles to see her cousin and at 20 mph. The trip took Ariella 2 hours. Then, Ariella drove from her cousin’s house and drove another 30 miles to the store at a speed of 10mph. It took Ariella 3 hours to arrive at the store. What was Ariella’s average speed for the trip?

17. Tracey ran to the top of a steep hill at an average pace of 6 miles per hour. She took the exact same trail back down. To her relief, the descent was much faster; her average speed rose to 14 miles per hour. If the entire run took Tracey exactly one hour to complete and she did not make any stops, what is the length of trail in miles one way?

18. A man bikes at a rate that is 6 miles/hour faster than the rate at which he jogs. After 30 minutes jogging and 90 minutes biking, the man has covered 21 miles. Over what distance was the man jogging?

19. Mike’s boat goes 12 miles per hour in still water. Find the rate of the current of the river if he can go 21 miles downstream in the same amount of time he can go 15 miles upstream.

20. An airplane can fly 550 miles with the wind in the same amount of time it takes to fly 425 miles against the wind. Find the speed of the wind, if the airplane is flying at a constant speed of 195 miles per hour.

21. A boat can go 15 miles against a current in the same time that it can go 25 miles with the current. The current is 4 miles per hour. Find the speed of the boat in still water.

22. With the wind, an airplane travels 1120 miles in seven hours. Against the wind, it takes eight hours. Find the rate of the plane in still air and the velocity of the wind.