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(3.2b) NOTES- System Word Problems

(3.2b) NOTES- System Word Problems. Ex: The Steele Canyon drama club is putting on a show. Student tickets cost $6 while adult tickets cost $8. If 200 total tickets were sold for $1,440, how many of those tickets were student tickets?. Let x= # of student tickets. Let y= # of adult tickets.

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(3.2b) NOTES- System Word Problems

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  1. (3.2b) NOTES- System Word Problems

  2. Ex: The Steele Canyon drama club is putting on a show. Student tickets cost $6 while adult tickets cost $8. If 200 total tickets were sold for $1,440, how many of those tickets were student tickets? Let x= # of student tickets Let y= # of adult tickets Set up system:

  3. Let x= # of student tickets Let y= # of adult tickets • the top equation represents amount of tickets. • the bottom equation represents value. • Solve the system using the substitution or • linear combination method. • Re-read the problem to see what it is • specifically asking for.

  4. -8 x + y = 200 -8x – 8y = –1600 6x + 8y = 1440 6x + 8y = 1440 –2x = -160 x = 80 80 + y = 200 y = 120 There were 80 student tickets sold.

  5. 1. The difference between two numbers is 11. The larger number is 3 less than two times the smaller number. Find the two numbers. x = bigger # x – y = 11 y = smaller # x = 2y – 3 x = 2y – 3 2y – 3 – y = 11 x = 2(14) – 3 y – 3 = 11 x = 28 – 3 y = 14 x = 25 The two numbers are 25 and 14.

  6. 2. Your cousin gave you a collection of 70 movies. Some are DVDs and the rest are VHS tapes. There are 6 more VHS tapes than 3 times the number of DVDs. How many of each type are in the collection. D = # DVD’s D + V = 70 V = # VHS’s V = 3D + 6 V = 3D + 6 D + 3D + 6= 70 V = 3(16) + 6 4D + 6 = 70 V = 48 + 6 4D = 64 V = 54 D = 16 There are 16 DVD’s and 54 VHS’s.

  7. 3. You invited 56 people to your graduation party. You can afford to rent 5 tables, round and/or rectangular. Each round table can seat 8 people and each rectangular table can seat 12 people. How many round and rectangular tables should you rent? x = # round tables y = # rect. tables -8 x + y = 5 –8x – 8y = –40 8x + 12y = 56 8x + 12y = 56 4y = 16 x + y = 5 y = 4 x + 4 = 5 x = 1 There is 1 round table and 4 rectangular tables.

  8. 4. A soccer team bought ice-cream cones to celebrate a victory. The total cost of 12 double cones and 8 single cones was $17. A double cone cost $0.25 more than a single cone. What was the price of each type of cone? 12D + 8S = 17 D = Cost of double cone D = S + 0.25 S = Cost of single cone 12(S + 0.25) + 8S = 17 D = S + 0.25 12S + 3 + 8S = 17 D = 0.70 + 0.25 20S + 3 = 17 D = 0.95 20S = 14 S = 0.70 A single costs 70¢ and a double costs 95¢.

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