MAFS Algebra 1. Equations and Inequalities in the Real-World. Day 6 - Student Packet

Transcription

1 MAFS Algebra 1 Equations Inequalities in the Real-World Day 6 - Student Packet

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3 Day 6: Equations Inequalities in the Real-World MAFS.912.A-CED.1.1 I CAN Write equations inequalities in one variable that represent real-world contexts. Problem Set Use the pictures below to answer questions Each square represents one tile, how many total tiles are in Step 5? Step 6? 2. What might you do to determine the number of tiles in Step 25? 3. Write a rule to predict the total number of tiles for any step. Show how your rule relates to the pattern. 4. Try to think of a different rule that you can use to predict the total number of tiles for any step. Show how your rule relates to the pattern. 5. Andrew also solved this problem came up with following equation:. How does each piece of his expression show up in the pattern? 6. Tami came up with the equation. How does each piece of her expression show up in the pattern? For the growing pattern below, each line segment is one unit in length. 7. How much total perimeter in Step 5? Step 6? (Remember to focus on the perimeter.) 8. How can you determine the amount of perimeter in Step 25? 9. Write a rule to predict the total amount of perimeter for any step. Show how your rule relates to the pattern. 10. Marsha also solved this problem came up with following expression: How does each piece of her expression show up in the pattern? 11. Tyler came up with the expression. How does each piece of his expression show up in the pattern? 1

4 Create an equation that describes each of the situations below, then solve. 12. The cost of a birthday party at Classic Boon is $200 plus $4 per person. The cost for Fletcher s party came to $324. How many people came to his party? 13. A cell phone company charges $55 per month for unlimited minutes plus $0.25 per text sent. If the charges to Dayne s cell phone for last month came to $100, how many texts did Aly send? 14. Aly has baked an apple pie wants to sell it in her bakery. She is going to cut it into 12 slices sell them individually. She wants to sell it for three times the cost of making it. The ingredients cost $8.50, she allowed $1.25 to cover the cost of electricity to bake it. Find the values for each of the following questions: a. What is the amount Aly will charge for each slice of pie? b. What is the total amount she will gross if she sells the entire pie? c. What will be the profit if she sells the entire pie? Creating Solving Real-World Problems 15. Jade is stred downtown with only $10 to get home. Taxis cost $0.75 per mile, but there is an additional $2.35 hire charge. Write a formula use it to calculate how many miles she can travel with her money. 16. Jasmin s Dad is planning a surprise birthday party for her. He will hire a bouncy castle, will provide party food for all the guests. The bouncy castle costs $150 for the afternoon, the food will cost $3 per person. Andrew, Jasmin s Dad, has a budget of $300. Write an equation use it to determine the maximum number of guests he can invite. 17. When Asia was young her Daddy marked her height on the door frame every month. Asia s Daddy noticed that between the ages of one three, he could predict her height (in inches) by taking her age in months, adding 75inches multiplying the result by one-third. Use this information to determine the following a. Write an equation linking her predicted height, h, with her age in months, m. b. Determine her predicted height on her second birthday. c. Determine at what age she is predicted to reach three feet tall. 18. Kashmir needs to fence in his puppy. He will fence in three sides, connecting it to his back porch. He wants the run to be 12 feet long he has 40 feet of fencing. How wide can Kashmir make his puppy enclosure? 19. Karen Sarah have bank accounts. Karen has a starting balance of $ is depositing $20 each week. Sarah has a starting balance of $43 is depositing $37 each week. When will the girls have the same amount of money? 20. I have enough money to buy five regular priced CDs have $6 left over. However all CDs are on sale today, for $4 less than usual. If I borrow $2, I can afford nine of them. How much are CDs on sale for today? 21. An emergency plumber charges $65 as a call-out fee plus an additional $75 per hour. He arrives at a house at 9:30 works to repair a water tank. If the total repair bill is $196.25, at what time was the repair completed? 22. A growers cooperative has a farmer s market in the town center every Saturday. They sell what they have grown split the money into several categories. 8.5% of all the money taken in is set aside for sales tax. $150 goes to pay the rent on the space they occupy. What remains is split evenly between the seven growers. How much total money is taken in if each grower receives a $175 share? 2

5 23. Shanice s car is traveling 10 miles per hour slower than twice the speed of Bron s car. She covers 93 miles in 1 hour 30 minutes. How fast is Bron driving? 24. A factory manager is packing engine components into wooden crates to be shipped on a small truck. The truck is designed to hold sixteen crates, will safely carry a 1200 lb cargo. Each crate weighs 12 lbs empty. How much weight should the manager instruct the workers to put in each crate in order to get the shipment weight as close as possible to 1200 lbs Solving Equations Inequalities 25. Write the correct inequality that models the following situation: The maximum allowed occupancy in a hotel room is 6 people. 26. Sarah is allowed to spend no more than $700 for lunch expenditure for company board meetings this week. Which is the correct inequality? 27. John needs to save more than $6,500 to renovate his master bedroom. Which inequality matches the situation? 28. The width of a rectangle plot is 12 feet. The area is greater than 89 square feet. Determine the inequality to match this situation. 29. Vivian wants to spend $75 or less on groceries. She already spent $37. How much more can she spend? 30. Jill is selling cookie boxes for The Girl Scouts. She wants to meet her goal of $750 or more. Each cookie box is sold for $5.50. What is the minimum number of cookie boxes Jill must sell to meet her goal? 31. Tom s wrestling goal is to be under 140 pounds. Find the inequality that matches this situation. 32. Thelma is driving to Los Angeles from San Jose. She has to drive at least 350 miles to arrive at her destination. She drove 110 miles for the first two hours. Determine the inequality that matches this situation. 33. Lisa s goal is to raise at least $25,000 for The Cure for Cancer extravaganza in February. Write the inequality that matches this situation. 34. The company is willing to budget at least $40,000 but no more than $50,000 training for their employees. There are 250 employees on site. Find the inequality that matches the amount the company is willing to spend for each employee. 35. The speed of a golf ball in the air is given by the formula, where is the time since the ball was hit. When is the ball traveling between inclusive? 36. The local amusement park sells summer memberships for $50 each. Normal admission to the park costs $25; admission for members costs $15. a. If Darren wants to spend no more than $100 on trips to the amusement park this summer, how many visits can he make if he buys a membership with part of that money? b. How many visits can he make if he does not? c. If he increases his budget to $160, how many visits can he make as a member? d. How many can he make as a non-member? 3

6 37. Jae just took a math test with 20 questions, each worth an equal number of points. The test is worth 100 points total. a. Write an equation relating the number of questions Jae got right to the total score he will get on the test. b. If a score of 70 points earns a grade of C-, how many questions would Jae need to get right to get a C- on the test? c. If a score of 83 points earns a grade of B, how many questions would Jae need to get right to get a B on the test? d. Suppose Jae got a score of 60% then was allowed to retake the test. On the retake, he got all the questions right that he got right the first time, also got half the questions right that he got wrong the first time. What percent did Jae get right on the retake? 4

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