Problem Solving with Three-Variable Systems

Transcription

1 Advanced Algebra CHAPTER 6.3 LINEAR SYSTEMS WITH THREE VARIABLES Name Period Date Problem Solving with Three-Variable Systems For each problem, define THREE VARIABLES for the three unknown quantities. Then write a system of THREE EQUATIONS which models the given situation. DO NOT SOLVE. COMPLETE THESE PROBLEMS ON A SEPARATE SHEET OF PAPER. 1. Joe Patriot has a piggy-bank filled with nickels, dimes, and quarters totaling $8.90. The piggy-bank contains 76 coins in all. The number of dimes is equal to the sum of the number of nickels and quarters. How many of each coin does he have? 2. Moe, Larry, and Curly went to Del Taco. Moe bought three tacos, two burritos, and one nacho and paid $9.50. Larry bought two tacos, two burritos, and two nachos and paid $9.00. Curly bought six tacos, four burritos and three nachos and paid $ What is the individual cost of each item? 3. The sum of the measures of the three angles in any triangle is 180 degrees. In triangle ABC the measure of angle A is twice the sum of the measures of angles B and C. The measure of angle B is three times the measure of angle C. What are the measures of the three angles? 4. At Edwards Theatre last night, 155 tickets were sold for the new movie. Adult tickets sold for $12, student tickets $8, and seniors $9, bringing in $1580 total. The number of adult tickets sold was four times the number of senior tickets. How many of each type of ticket were sold? 5. Yoda, Anakin, and Obi-Wan are combining their savings for a flight to the Death Star. Together, they have $680. Anakin has saved $20 less than Obi-Wan. Yoda has saved triple what the other two have saved put together. How much has each contributed to the total savings? SEE OTHER SIDE

2 COMPLETE THESE PROBLEMS ON A SEPARATE SHEET OF PAPER. For each problem, define THREE VARIABLES for the three unknown quantities. Then write and SOLVE a system of THREE EQUATIONS which models the given situation. 6. Stanley collects comic books. In his collection, he has 220 comics of the Batman, Ironman, and Spiderman titles. He has twenty more Spiderman comics than Ironman. The number of Batman comics is the same as the number of Spiderman. How many of each does he have? 7. At a pizza shop, two small pizzas, a liter of root beer, and a salad cost $14. One small pizza, a liter of root beer, and three salads cost $15. Three small pizzas and a liter of root beer cost $16. What is the cost of one small pizza? Of one liter of root beer? Of one salad? 8. On Sunday, January 22, 2006, Kobe Bryant of the Los Angeles Lakers scored 81 points, by making 46 baskets (a combination of 1-point free-throws, 2-points shots, and 3-pointers). Kobe made three times as many 2-point shots as 3-pointers. How many of each type of shot did Kobe make on that historic night? 9. Patty Patriot has 165 coins in her purse, comprised of pennies, nickels, and dimes. The total value of these coins is $4.50. The number of pennies is twice the sum of the number of nickels and dimes. How many of each type of coin does Patty have in her purse?

3 Let: n = the number of nickels d = the number of dimes q = the number of quarters n + d + q = 76 5n + 10d + 25q = 890 d = n + q Let: t = the cost of a taco b = the cost of a burrito n = the cost of a nacho Moe: 3t + 2b + 1n = 9.50 Larry: 2t + 2b + 2n = 9.00 Curly: 6t + 4b + 3n = 20.00

4 3. Let: A = angle A s measure B = angle B s measure C = angle C s measure A + B + C = 180 A = 2(B + C) B = 3C 4. Let: a = # of adult tickets s = # of student tickets x = # of senior tickets a + s + x = a + 8s + 9x = 1580 a = 4x

5 5. Let: y = Yoda s Savings a = Anakin s savings y + a + w = 680 a = w 20 y = 3(a + w) w = Obi-Wan s savings 6. Let: b = # of Batman Comics i = # of Ironman comics s = # of Spiderman comics b + i + s = 220 s = i + 20 b = s

6 7. Let: p = cost of a pizza r = cost of a root beer 2p + 1r + 1s = 14 1p + 1r + 3s = 15 3p + 1r = 16 s = cost of a salad 8. Let: x = # of 1-point free-throws y = # of 2-pointers z = # of 3-pointers Baskets: x + y + z = 46 Points: 1x + 2y + 3z = 81 y = 3z

7 9. Let: p = the number of pennies n = the number of nickels d = the number of dimes p + n + d = 165 1p + 5n + 10d = 450 p = 2(n + d )

8 Advanced Algebra HOMEWORK FOR LESSON 3.4C LINEAR SYSTEMS SOLUTIONS 1. Joe Patriot has a piggy-bank filled with nickels, dimes, and quarters totaling $8.90. The piggy-bank contains 76 coins in all. The number of dimes is equal to the sum of the number of nickels and quarters. How many of each coin does he have? 22 nickels, 38 dimes, and 16 quarters 2. Moe, Larry, and Curly went to Del Taco. Moe bought three tacos, two burritos, and one nacho and paid $9.50. Larry bought two tacos, two burritos, and two nachos and paid $9.00. Curly bought six tacos, four burritos and three nachos and paid $ What is the individual cost of each item? Taco $1.50, Burrito $2.00, and Nachos $ The sum of the measures of the three angles in any triangle is 180 degrees. In triangle ABC the measure of angle A is twice the sum of the measures of angles B and C. The measure of angle B is three times the measure of angle C. What are the measures of the three angles? A = 120, B = 45, C = At Edwards Theatre last night, 155 tickets were sold for the new movie. Adult tickets sold for $12, student tickets $8, and seniors $9, bringing in $1580 total. The number of adult tickets sold was four times the number of senior tickets. How many of each type of ticket were sold? 80 adult tickets, 55 student tickets, and 20 senior tickets 5. Yoda, Anakin, and Obi-Wan are combining their savings for a flight to the Death Star. Together, they have $680. Anakin has saved $20 less than Obi-Wan. Yoda has saved triple what the other two have saved put together. How much has each contributed to the total savings? Yoda $510, Anakin $75, Obi-Wan $95

9 6. Stanley collects comic books. In his collection, he has 220 comics of the Batman, Ironman, and Spiderman titles. He has twenty more Spiderman comics than Ironman. The number of Batman comics is the same as the number of Spiderman. How many of each does he have? 80 Batman, 60 Ironman, 80 Spiderman 7. At a pizza shop, two small pizzas, a liter of root beer, and a salad cost $14. One small pizza, a liter of root beer, and three salads cost $15. Three small pizzas and a liter of root beer cost $16. What is the cost of one small pizza? Of one liter of root beer? Of one salad? Pizza $5, Root Beer $1, Salad $3 8. On Sunday, January 22, 2006, Kobe Bryant of the Los Angeles Lakers scored 81 points, by making 46 baskets (a combination of 1-point free-throws, 2-points shots, and 3-pointers). Kobe made three times as many 2-point shots as 3-pointers. How many of each type of shot did Kobe make on that historic night? 18 free-throws, 21 two-pointers, and 7 three-pointers 9. Patty Patriot has 165 coins in her purse, comprised of pennies, nickels, and dimes. The total value of these coins is $4.50. The number of pennies is twice the sum of the number of nickels and dimes. How many of each type of coin does Patty have in her purse? 110 pennies, 42 nickels, 13 dimes