Once we have mastered solving a system of linear equations in two variables, we begin to look at their applications. For these problems, we will be setting up a system of linear equations that describes the given situation, and finding a solution to state our answer.
Test Objectives:•Demonstrate the ability to setup a linear system to describe a given scenario
•Demonstrate the ability to solve a system of linear equations
•Demonstrate the ability to check the solution for a system of linear equations
Applications of Linear Systems Test:
#1:
Instructions: Solve each word problem.
a) Going down the river, a boat went 9 mph. Going up the river, it only went 1 mph. Find the speed of the boat in still water along with the speed of the current.
#2:
Instructions: Solve each word problem.
a) Kristen's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 6 senior tickets and 2 student tickets for a total of $100. The school took in $109 on the second day by selling 5 senior tickets and 4 student tickets. Find the price of a senior ticket and the price of a student ticket.
#3:
Instructions: Solve each word problem.
a) A 40% fruit juice solution is going to be mixed with a 70% fruit juice solution to get 120 gallons of 50% fruit juice. How many gallons of each are needed?
#4:
Instructions: Solve each word problem.
a) Two trains which are 420 miles apart travel towards each other. They meet each other after 3.5 hours. What is the average speed of each train if one is moving 30 mph slower than the other?
#5:
Instructions: Solve each word problem.
a) Farmer Bill's Produce stand sells 20 pound bags of mixed nuts that contain 48% peanuts. To make his product he combines Krazy's mixed nuts which contain 60% peanuts and Clyde's mixed nuts which contain 30% peanuts. How much of each does he need to use?
Written Solutions:
Solution:
a) The speed of the boat in still water is 5mph, while the speed of the current is 4mph.
Solution:
a) The cost of a senior ticket is $13, while the cost of a student ticket is $11.
Solution:
a) 80 gallons of 40% fruit juice are needed along with 40 gallons of 70% fruit juice. This will make the required 120 gallons of 50% fruit juice.
Solution:
a) The faster train travels at 75mph, while the slower train travels at 45mph.
Solution:
a) He should use 12 pounds of Krazy's mixed nuts along with 8 pounds of Clyde's mixed nuts.