4-6 Writing Linear Equations for Word Problems

1. 4-6 Writing Linear Equations for Word Problems Give a problem that has y-intercept like in the sample problem. Problems in alignment with handout. Algebra 1 Glencoe McGraw-Hill Linda Stamper

2. There are two basic types of real-life problems that can be solved with linear equations. Type I Problems involving a constant rate of change (slope). (Write equation in slope-intercept form.)

3. There are two basic types of real-life problems that can be solved with linear equations. Type I Problems involving a constant rate of change (slope). (Write equation in slope-intercept form.) Type II Problems involving two variables, x and y, such that the sum of Ax + By is a constant. (Write equation in standard form.)

4. You open a savings account with $150. You plan to add $50 each month. Write an equation that gives the monthly savings, y (in dollars), in terms of the month, x. y No graph is given. Can you visualize the graph in your head? • (5,400) (3,300) • savings (dollars) If the y-intercept is not given, what piece of information would you need? • 100 a point 50 x If the slope is not given, what information would you need? 1 2 0 months What is the equation of this line? two points

5. Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $40 per year. In 1985, the rent was $300 per month. Write an equation that gives the monthly rent y (in dollars), in terms of the year x. Let year 0 correspond to 1980.

6. Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $40 per year. In 1985, the rent was $300 per month. Write an equation that gives the monthly rent y (in dollars), in terms of the year x. Let year 0 correspond to 1980. Assign Labels: Let x = years Let y = monthly rent in dollars Find the constant rate of change (slope). Think of a point on the graph that represents 1985 and $300. y Write an equation. (5,300) • rent (dollars) x years 1980

7. Recall value problems. Andrea has 52 coins in dimes and quarters worth $10. How many of each coin does she have? Number Labels and Value Labels Let d = number of dimes Let 52 –d = number quarters Let .10d = value of the dimes Let .25(52 –d) = value of quarters Verbal Model. Value of dimes + Value of quarters = Total Value Write the equation. .10d +.25(52 – d) = 10 Today you will write a linear equation that has two variables to represent a word problem. Type II Problems involving two variables, x and y, such that the sum of Ax + By is a constant.

8. Mrs. Burke’s drama class is presenting a play next Friday night and you have been put in charge of ticket sales. Tickets for adults are sold for $4 each and students pay $2 each. Write a linear equation, in standardform, that models the different number of adult tickets, x, and the number of student tickets, y, that could be sold if total ticket sales are $320.

9. Mrs. Burke’s drama class is presenting a play next Friday night and you have been put in charge of ticket sales. Tickets for adults are sold for $4 each and students pay $2 each. Write a linear equation, in standardform, that models the different number of adult tickets, x, and the number of student tickets, y, that could be sold if total ticket sales are $320. Number Labels and Value Labels Let x = number of adult tickets Let y = number of student tickets Let 4x = value of adult tickets Let 2y = value of student tickets Verbal model. Value of adult + value of student = total value of tickets tickets tickets Write the equation.

10. Example 1 Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $20 per year. In 1987, the rent was $350 per month. Write an equation that gives the monthly rent y (in dollars), in terms of the year x. Let year 0 correspond to 1980.

11. Example 1 Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $20 per year. In 1987, the rent was $350 per month. Write an equation that gives the monthly rent y (in dollars), in terms of the year x. Let year 0 correspond to 1980. Assign Labels Let x = years Let y = monthly rent in dollars Find the constant rate of change (slope). Think of a point on the graph that represents 1987 and $350. y Write an equation. (7,350) • rent (dollars) x years 1980

12. Example 2 You are flying from LA to Boston. Three hours into the trip you have traveled 825 miles. You are traveling at an average speed of 275 mph. Write a linear equation that gives the distance y (in miles), after x hours of flying.

13. Example 2 You are flying from LA to Boston. Three hours into the trip you have traveled 825 miles. You are traveling at an average speed of 275 mph. Write a linear equation that gives the distance y (in miles), after x hours of flying. Assign Labels Let x = hours flying Let y = distance in miles Find the constant rate of change (slope). Think of the point on a graph that represents 3hrs and 825 mi. y Use point-slope to write an equation. distance (3,825) • x hours

14. Example 3 By the end of your 5th French lesson you have learned 20 vocabulary words. After 10 lessons you know 40 vocabulary words. Write an equation that gives the number of vocabulary words you know y, in terms of the number of lessons you have had x. Assign Labels Let x = # lessons Let y = # vocab. words Find the slope. Write an equation.

15. Example 4 Joan earns $4 an hour when she works on Fridays, and $6 an hour on Saturdays. Write a linear equation that models the different number of hours she could have worked on each of the two days if she earned $36. If x (Friday’s hours) and y (Saturday’s hours) are whole number, find all the possible combinations she could have worked on Friday and Saturday.

16. Example 4 Joan earns $4 an hour when she works on Fridays, and $6 an hour on Saturdays. Write a linear equation that models the different number of hours she could have worked on each of the two days if she earned $36. If x (Friday’s hours) and y (Saturday’s hours) are whole number, find all the possible combinations she could have worked on Friday and Saturday. Let x = Fri. hours Let y = Sat. hours Assign number labels. Let 4x = Fri. earn. Let 6y = Sat. earn. Assign earning labels. Verbal model. Friday’s earn. + Saturday’s earn. = total earn. Write the equation.

17. Example 4 Joan earns $4 an hour when she works on Fridays, and $6 an hour on Saturdays. Write a linear equation that models the different number of hours she could have worked on each of the two days if she earned $36. If x (Friday’s hours) and y (Saturday’s hours) are whole number, find all the possible combinations she could have worked on Friday and Saturday. y Make a table. Sat. hours (0,6) • (3,4) • (6,2) • (9,0) • x Friday hours

18. Example 5 You want to buy some CDs and Videos for the Teen Center recreation room. You have $75 to spend. You can order CDs for $15 each and Videos for $5 each from your discount catalog. Write a linear equation that models the different number of CDs and Videos you could purchase. If x (number of CDs) and y (number of Videos) are whole numbers, find all the possible combinations you could purchase. Assign # labels. Let x = # CDs Let y = # Videos Assign cost labels. Let 15x = cost of CDs Let 5y = cost of Videos Verbal model. Cost of CDs + Cost of Videos = total cost Write the equation.

19. y Make a table and graph. • • • • # of Videos • • x # of CDs The ordered pairs represent the possible combinations. (0,15), (5,0), (1,12), (2,9), (3,6), (4,3)

20. Practice 1 You collect comic books. In 1990 you had 60 comic books. By the year 2000 you had 240 comic books. Find an equation that gives the number of comic books y, in terms of the year, x. Let year 0 correspond to 1990. Practice2 Maria decides to start jogging every day at the track. The first week she jogs 4 laps. She plans to increase her laps by one lap per week. Let y represent the number of laps Maria runs and let x represent the number of weeks she’s running. Write a linear equation that gives the number of laps she is running after x weeks.

21. Practice 1 You collect comic books. In 1990 you had 60 comic books. By the year 2000 you had 240 comic books. Find an equation that gives the number of comic books y, in terms of the year, x. Let year 0 correspond to 1990. Assign Labels Let x = year Let y = # comic books Use slope-intercept to write an equation. Identify two points.

22. Practice 2 Maria decides to start jogging every day at the track. The first week she jogs 4 laps. She plans to increase her laps by one lap per week. Let y represent the number of laps Maria runs and let x represent the number of weeks she’s running. Write a linear equation that gives the number of laps she is running after x weeks. Assign Labels Let x = # weeks Let y = # laps Find the slope. Identify a point. Use point-slope to write an equation.

23. Homework 4-A13 Handout A13