# Application of Linear Equations

Video solutions to help Grade 8 students learn how to rewrite an exponential expression that represents a series as a linear equation.

## New York State Common Core Math Module 4, Grade 8, Lesson 9

### Lesson 9 Outcome

• Students know how to rewrite an exponential expression that represents a series as a linear equation.

### Lesson 9 Summary

• We can rewrite equations to develop a pattern and make predictions.
• We know that for problems like these we can generalize equations so that we do not have to do each step to get our answer.
• We learned how equations can be used to solve problems.

### NYS Math Module 4 Grade 8 Lesson 9 Exercises

Exercises 3 - 11
3. Marvin paid an entrance fee of \$5 plus an additional \$1.25 per game at a local arcade. Altogether he spent \$26.25. Write and solve an equation to determine how many games Marvin played.

4. The sum of four consecutive numbers is -26. What are the numbers?

5. A book has x pages. How many pages are in the book if Maria read 45 pages of a book Monday, 1/2 the book Tuesday, and the remaining 72 pages Wednesday?

6. A number increased by 5 and divided by 2 is equal to 75.

7. The sum of thirteen and twice a number is seven less than six times a number. What is the number?

8. The width of a rectangle is 7 less than twice the length. If the perimeter of the rectangle is 43.6 inches, what is the area of the rectangle?

9. Two hundred and fifty tickets are available for sale for a school dance. On Monday 35 tickets were sold. An equal number of tickets were sold each day for the next 5 days. How many tickets were sold on one of those days?

10. Shonna skateboarded for some number of minutes on Monday. On Tuesday, she skateboarded for twice as many minutes as she did on Monday, and on Wednesday, she skateboarded for half the sum of minutes from Monday and Tuesday. Altogether she skateboarded for a total of 3 hours. How many minutes did she skateboard each day?

11. In the diagram below, △ABC ∼ △A'B'C'. Determine the length of AC and BC.