After mastering linear equations in one variable, the next step is to learn how to tackle real world problems. These are known as application problems or word problems. These problems require us to cipher through key information and create and solve an equation to gain our answer.
Test Objectives:•Demonstrate the ability to find the main objective in a word problem
•Demonstrate the ability to setup an equation when solving a word problem
•Demonstrate the ability to report the answer and ensure the result is reasonable
Applications of Linear Equations II:
#1:
Instructions: Solve each word problem.
a) Jessica wants to make 5 gallons of a 31% acid solution by mixing together a 15% acid solution and a 65% acid solution. How much of each solution must she use?
#2:
Instructions: Solve each word problem.
a) Vegetable oil which costs $2.44 per pound is made by combining soybean oil which costs $3.45 per pound with canola oil which costs $2.10 per pound. Find the amount in pounds of soybean and canola oil required to make 13.5 pounds of vegetable oil.
#3:
Instructions: Solve each word problem.
a) Eduardo left the mall and traveled toward his cabin on the lake at an average speed of 37.1mph. Nancy left 3.2 hours later and traveled in the opposite direction with an average speed of 62mph. How long does Nancy need to travel before they are 297.1 miles apart?
#4:
Instructions: Solve each word problem.
a) Dan drove to the train station and back. It took 2.7 hours longer to go there than it did to come back. The average speed on the trip there was 31.5mph. The average speed on the trip back was 72mph. How many hours did the trip there take?
#5:
Instructions: Solve each word problem.
a) Angel left the mall and traveled toward the street fair at an average speed of 52 miles per hour. Will left 1.2 hours later and traveled in the same direction, but with a speed of 67.6 miles per hour. Find the number of hours Angel traveled before Will caught up.
Written Solutions:
Solution:
a) She needs to use 3.4 gallons of the 15% acid solution, along with 1.6 gallons of the 65% acid solution.
Solution:
a) They need to use 3.4 pounds of soybean oil along with 10.1 pounds of canola oil.
Solution:
a) Nancy needs to travel for 1.8 hours before they are 297.1 miles apart.
Solution:
a) The trip there took 4.8 hours.
Solution:
a) Angel travels for 5.2 hours before Will caught up.