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Math 8H

Problem Solving Using Linear Equations Heath text, section 5.7. Math 8H. Algebra 1 Glencoe McGraw-Hill JoAnn Evans. Four types of linear equation word problems that will be solved in this lesson are:. Y-Intercept/Slope Problems.

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Math 8H

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  1. Problem Solving Using Linear Equations Heath text, section 5.7 Math 8H Algebra 1 Glencoe McGraw-Hill JoAnn Evans

  2. Four types of linear equation word problems that will be solved in this lesson are: Y-Intercept/Slope Problems Point/Slope Problems Point / Point problems Standard Form problems

  3. When solving word problems: • identify the recognizable elements and label them. • show the proper support work for the equation. • use the equation to answer other parts of the question. • remember that word problems need word answers.

  4. Y-Intercept / Slope Problem: A stereo sales person is paid a base salary of $500 per month plus 7% commission on the amount of stereo equipment he sells each month. Write a linear model that shows his salary, y, in terms of the amount of his sales, x, each month. Use the equation to predict how much his November paycheck will be if he sells $35,000 worth of equipment that month. What is the rate of change for the sales person’s salary? What does the term base salary mean?

  5. The slope is .07, the decimal form of 7% because that’s the rate of increase for his pay for each dollar of equipment he sells. The y-intercept is 500 because even if he doesn’t sell any stereo equipment (sales = 0), he will still earn the base salary of $500. b = 500 m = .07 If the slope and y-intercept are both known, you can write the equation in slope-intercept form: y = .07x + 500

  6. Use the equation to predict how much his November paycheck will be if he sells $35,000 worth of equipment that month. y = .07(35,000) + 500 y = 2450 + 500 y = 2950 The November paycheck will be $2950 for the salesman.

  7. A photographer charges $50 for a sitting and a basic package of photos. Additional 5 x 7 pictures cost $12 each. Write a linear equation which gives the total cost in dollars, y, in terms of how many extra 5 x 7 pictures you purchase, x. What is the rate of change? The number of extra 5 x 7 pictures ordered will change the cost at the rate of $12 per picture. + Total cost = $12 # of extra 5 x 7 pictures sitting & basic package  y = 12x + 50

  8. Point - Slope Problem: Between 1980 and 1995 the amount spent on advertising by the Locktite company increased by approximately $480 per year. In 1986 the company spent $12,000 on advertising. Find an equation that gives the total amount spent on advertising, A, in terms of the year, t. Let t = 0 correspond to the year 1980. Predict the amount that was spent in 1992. The company spent $12,000 in 1986. How is this information useful? What is the rate of change for the advertising budget?

  9. The slope will be 480 because that’s the rate of increase per year in the $ spent on advertisements. The point will be the information that describes the year 1986, the 6th year, when sales were $12,000. (t, A) (6, 12000) m = 480 Use y = mx + b to write an equation now that you know the slope and a point. A = 480t + b 12,000 = 480(6) + b 12,000 = 2880 + b 9,120 = b A = 480t + 9120

  10. Predict the amount that was spent in 1992. A = 480t + 9120 1992 is year 12: A = 480(12) + 9120 A = 5760 + 9120 A = 14,880 I predict the company will spend $14,880 on advertising in 1992.

  11. Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $20 per year. In 1987, the rent was $350 a month. Find an equation that gives the monthly rent in dollars, y, in terms of the year, t. Let t = 0 correspond to 1980. What is the rate of change for the rent? There is information about the rent in one particular year. m = 20 If 1980 is the “0” year, what year is 1987? y = mx + b (year, rent) (7, 350) 350 = 20(7) + b 350 = 140 + b 210 = b What was the rent in 1980? What was the rent in 1989?

  12. Two Point Problem: On January 1, Spike had a savings account balance of $2742. By April 1, his balance had increased to $3597. Write a linear equation showing the amount in his account, A, in terms of the month, t. Think of the months numbered with January as month 1 and April as month 4. What will the account balance be by August if it continues to increase at the same rate? There’s enough information here to name two points (t, A). Name the two points.

  13. The points will be (1, 2742) and (4, 3597). Calculate the slope between the two points. Use the slope and one of the two points to write the equation of the line: (t, A) (4, 3597) (1, 2742) A = mt + b 2742 = 285(1) + b b = 2457 A = 285t + 2457 m = 285

  14. Use the equation to answer the remaining question. What will the account balance be by August if it continues to increase at the same rate? A = 285t + 2457 A = 285(8) + 2457 A = 4737 By August his account will hold $4737.

  15. The population of Laredo, Texas, was about 197,000 in 2003. It was about 123,000 in 1990.Write a linear equation to describe the changes in the population, P, in terms of the year, x. Let x = 0 correspond the year 1990. Round the slope to the nearest whole number. The P-intercept is already known. In the “0” year for this situation, the population was 123,000. (x, P) (13, 197,000) (0, 123,000) P = 5692x + 123,000 What was Laredo’s population in the year you were born?

  16. Standard Form Problem: A fruit stand at the Farmer’s Market is selling Granny Smith apples for $4 a pound and blackberries for $6 a pound. Write a linear equation showing the possible number of pounds of apples, a, and pounds of blackberries, b, that were sold on Thursday if total sales for the day were $336. Use the equation to find the # of pounds of blackberries sold if 10 pounds of apples were sold. Let a = # lbs. apples Let b = # lbs. blackberries Let 4a = value of apples Let 6b = value of blackberries

  17. Value of apples + Value of berries = Total 4a + 6b = 336 Use the equation to find the # of pounds of blackberries sold if 10 pounds of apples were sold. 4A + 6B = 336 4(10) + 6B = 336 6B = 296 B = 49.3 49.3 pounds of blackberries were sold at the fruit stand.

  18. Grandma Williams made 240 oz. of jelly. She used two different types of jars for the jelly. The first type held 10 oz. and the second type held 12 oz. Write an equation that represents the different numbers of 10 oz. jars, x, and 12 oz. jars, y, that will hold all of the jelly. Let x = # small jars Let y = # larger jars Let 10x = # oz in small jars Let 12y = # oz in larger jars 10x + 12y = 240 Find the 2 combinations in the number of jars that would work as a solution.

  19. Put the equation in slope-intercept form. x y 0 +6 -5 6 12 18 24

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