Systems Word Problems
Grade 8 · Math · Systems of Equations · Iowa, USA
Lesson Summary
Translate real-world situations into systems of equations and solve them.
Explanation
Many real-life problems can be modeled with two equations and two unknowns. The key is to define your variables clearly, write an equation for each piece of information, and then solve the system. For example, if tickets for adults and children cost different amounts and you know the total number of tickets and the total cost, you can set up two equations to figure out how many of each were sold.
Practice Questions
Q1: Adult tickets cost $8 and child tickets cost $5. A total of 20 tickets were sold for $130. How many of each?
Answer: Let a = adults, c = children. a + c = 20 and 8a + 5c = 130. Solving gives a = 10 and c = 10.
Q2: The sum of two numbers is 25 and their difference is 7. What are the numbers?
Answer: x + y = 25 and x − y = 7. Adding gives 2x = 32, x = 16, y = 9.
Q3: A store sells pens for $2 and notebooks for $5. You buy 6 items for $21. How many of each?
Answer: p + n = 6 and 2p + 5n = 21. From the first equation p = 6 − n. Substituting: 12 − 2n + 5n = 21, 3n = 9, n = 3, p = 3.
People Also Ask
What is Systems Word Problems in Grade 8 Math?+
Systems Word Problems is a lesson in the Systems of Equations chapter of Grade 8 Math. It is part of the Iowa, USA school curriculum and covers key concepts that students need to understand at this level.
What grade level covers Systems Word Problems?+
Systems Word Problems is taught in Grade 8 as part of the Math curriculum in Iowa, USA.
How can I help my child with Systems of Equations in Math?+
Start with the lesson summary and explanation on this page. Practice the questions provided, then use TutorTom for personalized, step-by-step help with Systems of Equations topics.