About Applications of Linear Systems:
To solve a word problem that involves a system of linear equations, we use our six-step procedure: Read the problem and determine the objective, assign a variable to each unknown, write a system of equations that describes the given scenario, solve the system, state the answer, and check the result.
Test Objectives
- Demonstrate the ability to solve a linear system in two variables
- Demonstrate the ability to solve a linear system in three variables
- Demonstrate the ability to solve a word problem that involves a system of linear equations
#1:
Instructions: Solve each word problems.
a) Leo's school is selling tickets to the annual dance competition. On the first day of ticket sales, the school sold 4 adult tickets and 5 child tickets for a total of $101. The school took in $167 on the second day by selling 10 adult tickets and 3 child tickets. What is the price each for one adult ticket and one child ticket?
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#2:
Instructions: Solve each word problems.
a) Kayla and James are selling pies for a school fundraiser. Customers can buy blueberry pies and blackberry pies. Kayla sold 11 blueberry pies and 7 blackberry pies for a total of $217. James sold 15 blueberry pies and 16 blackberry pies for a total of $425. Find the cost of one blueberry pie and one blackberry pie.
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#3:
Instructions: Solve each word problems.
a) A plane traveled 1214.84 miles to San Francisco and back. The trip there was with the wind and took 12.1 hours. The trip back was against the wind and took 25.1 hours. What was the speed of the plane in still air? What was the speed of the wind?
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#4:
Instructions: Solve each word problems.
a) A boat traveled 158.4 miles downstream and back. The downstream trip took only 8 hours. The trip back took 66 hours. Find the speed of the boat in still water, and the speed of the current.
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#5:
Instructions: Solve each word problems.
a) A car company produces three models only: A, B, and C. Each model A requires 2 hours of welding, 2 hours of assembling, and 1 hour of painting. For model B, the amounts are: 1, 3, and 1 (welding, assembling, and painting). Lastly, Model C, requires 3, 2, and 2 (welding, assembling, and painting). Assume that 100 hours are available for welding, 100 hours for assembly, and 65 hours for painting. How many of each type of car should be produced?
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Written Solutions:
#1:
Solutions:
a) A child ticket is sold for $9, while an adult ticket is sold for $14.
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#2:
Solutions:
a) A blueberry pie costs $7 and a blackberry pie costs $20.
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#3:
Solutions:
a) The plane travels at 74.4 mph in still air, and the wind speed is 26 mph.
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#4:
Solutions:
a) The boat speed in still water is 11.1 mph and the current is moving at a speed of 8.7 mph.
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#5:
Solutions:
a) 15 model A cars should be produced, along with 10 model B cars, and 20 model C cars.
