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Chapter 4.3: Solving Applications of Systems of Linear Equations in 2 Variables
- The combined land area of my neighbor’s property and mine is 139,973 square feet. The difference between the two land areas of our properties is 573 square feet. If my neighbors have the larger land area, determine the land area of each of our properties.
Let ___ = ______________________________________
Let ___ = ______________________________________
Equations:
Answers: 69,700 sq. ft. = my property 70,273 sq. ft. = my neighbor’s property
- At a professional football game, the cost of 2 bottles of water and 3 pretzels is $16.50. The cost of 4 bottles of water and 1 pretzel is $15.50. Determine the cost of a bottle of water and the cost of a pretzel.
Let ___ = ______________________________________
Let ___ = ______________________________________
Equations:
Answers: $3 = water bottle $3.50 = pretzel
- Say you have a 512-MB memory card and a 4-GB memory card for your digital camera. Together the two memory cards can store a total of 1042 photos. The 4-GB memory card can store 10 more than seven times the number of photos the 512-MB memory card can store. How many photos can each memory card store?
Let ___ = ______________________________________
Then ___________ = _____________________________
Equation:
Answers: 129 photos = 512-MB 913 photo = 4-GB
- A rowing team, while practicing, rowed an average of 16.7 miles per hour with the current and 9.7 miles per hour against the current. Determine the team’s rowing speed in still water and the speed of the current.
Let ___ = ______________________________________
Let ___ = ______________________________________
Equations:
Answers: 13.2 mph = the team’s rowing speed in still water 3.5 mph = the speed of the current
- A guy and a girl were hanging out in Santa Cruz. Afterwards, the girl drives home to Scotts Valley at an average speed of 60 miles per hour and the guy drives home to Watsonville at an average speed of 50 miles per hour. If the sum of their driving times is 0.56 hours and if the sum of the distances driven is 30 miles determine the time each person spent driving home.
Let ___ = ______________________________________
Let ___ = ______________________________________
Equations:
Answers: 0.36 hours = the guy’s time 0.2 hours = the girl’s time
- Job A pays an annual salary of $38,000 with a pay increase of $1000 each year. The annual salary for Job A, A ( t ),is the function A ( t ) 1000 t 38000 , where t is the number of years since 2010. Job B pays an annual salary of $45,500 with a pay increase of $500 each year. The annual salary for Job B, B ( t ),is the function B ( t ) 500 t 45500 , where t is the number of years since 2010. Solve the system of equations to determine the year both salaries will be the same. What will be the salary in that year?
Answer: In 2025 both salaries will be $53,000 per year
