Fall Break Packet Unit 2

Transcription

1 Fall Break Packet Unit 2 Solve each equation. 1) 4(-3b + 7) = 16 8b 2) -4(-2n + 1) = n ) 3(7 6p) = p 4) 5(n 2) = n 5) n = -n + 4(6n + 7) 6) -(2 + 8n) = 6n + 40 Solve each inequality. 9) v 6(4v + 5) 8v 10) -3(n + 4) 7 < -7n 19 11) x < 2x + 5(x 1) 12) 8x (4 + 3x) 5 Solve each system by substitution. 13) 11x 5y = 28 14) 8x + 4y = 28 y = -5x 20 y = -7x + 2

2 15) -11x 7y = 21 16) y = 6x - 3 y = 12x 3-18x + 3y = ) y = 10x 19 18) -10x 6y = x 3y = -27 y = 3x Solve each system by elimination. 19) 12x + 8y = ) -5x 2y = -4 6x + 7y = 6 15x 6y = ) -3x + y = 4 22) -4x 6y = 12 7x + 9y = 2 9x + 4y = -8 23) 4x + 4y = ) -10x 30y = 0-10x 3y = 26 16x + 48y = 0

3 Write an equation to solve. 1. Celia and Ryan are starting a nutrition program. Celia currently consumes 1200 calories a day and will increase that number by 100 calories each day. Ryan currently consumes 3230 calories a day and will decrease that number by 190 each day. They will continue this pattern until they are both consuming the same number of calories per day. In how many days will that be? 2. A moving company charges $800 plus $16 per hour. Another moving company charges $720 plus $21 per hour. How long is a job that costs the same no matter which company is used? 3. Aaron needs to take out a loan to purchase a motorcycle. At one bank, he would pay $2500 initially and $150 each month for the loan. At another bank, he would pay $3000 initially and $125 each month. After how many months will the two loan payments be the same? 4. What equation models this story? Suppose you write a book. The printer charges $4 per book to print it, and you spend $5500 on advertising. You sell the book for $15 a copy. How many copies do you need to sell to break even? a. 15x = 4x b. 4x = 15x Write an inequality to solve. c. 4x 5500 = 15x d. 15x 4x = Rosa has decided to sell pet rocks at an art fair for $5 each. She has paid $50 to rent a table at the fair and it costs her $2 to package each rock with a set of instructions. For what numbers of sales will Rosa make a profit? 6. Sophia types 75 words per minute and is just starting to write a term paper. Patton already has 510 words written and types at a speed of 60 words per minute. How long will it take for Sophia to type and have a longer term paper than Patton? 7. Jamie has a job paying $25,000 and expects to receive a $1000 raise each year. Wei has a job paying $19,000 a year and expects a $1500 raise each year. For what span of time is Jamie making more money than Wei? 8. What inequality models this story? Keith is racing his little sister Pattie and has given her a 15 foot head start. She runs 5 ft/sec and he is chasing at 8 ft/sec. For how long can Pattie stay ahead of Keith? a x < 8x c x > 8x b. 15 5x < 8x d. 15 5x > 8x

4 Write a system of equations and find the intersection. Then explain what your solution means in context. 9. Maribel has $1.25 in her pocket. The money is in quarters and dimes. There are a total of 8 coins. How many quarters and dimes does Maribel have in her pocket? 10. Fabulously Fit offers memberships for $35 per month plus a $50 enrollment fee. The Fitness Studio offers memberships for $40 per month plus a $35 enrollment fee. In how many months will the fitness clubs cost the same? What will the cost be? 11. Kate bought 3 used CDs and 1 used DVD at the bookstore. Her friend Joel bought 2 used CDs and 2 used DVDs at the same store. If Kate spent $20 and Joel spent $22, determine the cost of a used CD and a used DVD. 12. What system of equations models this story? Mr. Nguyen bought a package of 3 chicken legs and a package of 7 chicken wings. Ms. Dawes bought a package of 3 chicken legs and a package of 6 chicken wings. Mr. Nguyen bought 45 ounces of chicken. Ms. Dawes bought 42 ounces of chicken. How much did each chicken leg and each chicken wing weigh? 3x + 3y = 45 3x + 7y = 42 a. { c. { 7x + 6y = 42 3x + 6y = 45 3x + 3y = 42 3x + 7y = 45 b. { d. { 7x + 6y = 45 3x + 6y = The Lees spent $31 on movie tickets for 2 adults and 3 children. The Macias spent $26 on movie tickets for 2 adults and 2 children. What are the prices for adult and child movie tickets? 14. A local school sold attracted 230 audience members to its production of Hamlet. They made $1522 from $8 ticket sales but only charged students $5. How many audience members were not students of the school? 15. What system of equations models this story? A sales person that worked at a cell phone store is responsible for selling $150 Android phones and $200 iphones. He knows he sold 24 phones for a total of $4150. How many of each phone did he sell? x + y = 24 a. { 150x + 200y = x + 24y = 4150 b. { 150x + 200y = 4150 x + y = 4150 c. { 150x + 200y = x + y = 24 d. { 200x + y = 4150

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