XEI 502 LESSON/NOTES CRS SKILL Expressions Equations and Inequalities XEI 502 Period____________ Name_________________________________________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION XEI 404 Perform straight forward word-­‐to-­‐symbol translations Level 2 – MOST students will XEI 502 Write expressions, equations, or inequalities attain mastery of the focus skill in with a single variable for common pre-­‐algebra isolation. settings Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will XEI 602 Write expressions, equations, and attain mastery of the extension inequalities for common algebra settings skill. VOCABULARY Inequality REQUIRED SKILL TO MASTER ON KHAN Writing expressions ADDITIONAL PRACTICE ON KHAN Writing expressions 2 Writing expressions with variables word problems Level 1 Translate the following into an algebraic expression: 1. The sum of 12 and the product of a number and 3: 2. 78 subtracted from a number: 3. Ninety decreased by the product of a number and 12: 4. Half of a number increased by 6: 5.
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of the sum of a number and 2: 7
6. Eight less than a number: 7. Five more than the quotient of a number and 8: 1 Key words in mathematical phrases. Addition increased by more than combined, together total of sum, plus added to greater Subtraction decreased by minus, less difference between/of less than, fewer than subtract diminished reduced Multiplication of times, multiplied by product of percent of increased/decreased by a factor of (this type can involve both addition or subtraction and multiplication!) Division per, a out of ratio of, quotient of percent (divide by 100) Equals is, are, was, were, will be gives, yields sold for equal results Directions: Define the variable(s), and then write an equation to model each situation. 8. The total cost of lunch is $5.50 times the number of people at the table. 9. The area of a rectangle is 12cm times the length of the rectangle. 10. The cost of a telephone call is 75 cents plus 25 cents times the number of minutes. 2 11. The total length of the edges of a cube is 12 times the length of an edge. 12. Marcus buys three notebooks for school. Each notebook is the same price. Marcus uses a coupon that is worth $2 off his total purchase. He pays a total of $7 with the coupon. Level 2 13. The sum of two consecutive even integers 14. Five is three more than a number 15. Five times the difference of a number and 4 16. Ten subtracted from 10 times a number is that number plus 5 17. First consider the expression for: The sum of 4 and the product of 3 and x. Now write an expression for the quotient of the above expression and 7. 18. First consider the expression for: Take the product of 7 and x and add 3. Now write an expression for the product of 6 and the above expression. 19. An earring manufacturing company has fixed costs of $10,000 per month and production costs
of $0.60 for each pair of earrings it makes. If the company produces x pairs of earrings in a
month, write an expression to represent the total of the company’s monthly costs?
20. A truck sprang a leak at the bottom of its radiator, which held 480 ounces of fluid when it
started to leak, and started losing radiator fluid at a constant rate of 4 ounces per minute. Write
an expression to represent the number of ounce of fluid in the radiator t minutes after it sprung a
leak.
3 21. Mr. Vasu has an aquarium of African Cichlids. The length of his fish is 5 inches longer than
twice its fins. Write an expression for the length of the fish where x is the length of a fin. 22. Michael can spend at most $4.10 for lunch. He buys a hamburger and a drink for $2.75. Write an inequality that models how much Michael can spend on dessert and stay within he spending limit. 23. Jerry has only $27 for school supplies. He spends $18 on a backpack. Write an inequality that models how much more money Jerry can spend on school supplies and stay within his limit. 24. A school auditorium can seat 450 people for graduation. The graduates will use 74 seats. Write an inequality to describe the number of additional people who can be seated in the auditorium. 4 Level 3 25. The diaper service where you work bills customers once a week. Each week, it charges $0.40 each for the first 75 diapers used, and $0.25 each for any additional diapers. Let d represent any additional diapers beyond 75. a. Write an algebraic expression for how much money the diaper service makes in one week? b. Evaluate how much money the diaper service makes if it washes 125 diapers in a week? 26. Suppose that a rental shop charges an $8 fee plus $3 per hour to rent a bike. a. Write an algebraic equation for how much the rental will cost (C) if you rent a bike for (H) hours. b. If you have $20 to spend how many hours can you afford to rent the bike? 27. In 1990 the United Nations reported a deforestation figure of around 114,364 acres of trees per day. a. Write an equation that finds the number of acres of trees that have been deforested (A) given the number of days (D). b. Use the equation above to find how long it would take to lose an area of forest equal to the area of the Olympic National Park if it is 922,654 acres of forest. Level 4 28. Kim, Carrie, and Christina had part-­‐time jobs at Burger Heaven. Kim earned twice as much as Cristina, and Carrie earned $24 more then Christina. If x represent the amount Christian earned. Write an expression that represent the total amount earned by all 3 employees. 5 29. A catering business specializes in catering wedding receptions. They charge $550 for setting up the buffet and an additional $12.50 per guest. Mr. and Mrs. Hiroshige want to spend no more than $2,400 on the catering for their daughter’s wedding reception. a. Write an inequality in terms of the number of guests, g, that they can invite to the reception. b. Solve the inequality to determine the maximum number of guests they can invite. 30. Hajime takes his vacuum cleaner to the repair shop. The woman at the repair shop generally
charges $15 per hour for her labor. She tells Hajime to expect to pay more than $45 for the
repair. Write an inequality for finding an estimate of how long fixing the vacuum cleaner will take.
31. According to the bus schedule, a bus stops at the corner of 2nd Street and 9th Street every thirty
minutes, on the half hour. The bus is sometimes up to five minutes late. Your watch says it is
3:50 PM. Write an inequality to express the amount of time you may wait for the bus.
32. Kamisha got several bills in the mail today: her rent, which is $425; her water bill, which is $25;
and her phone bill, which is $15. She says she has more than enough money in the bank to cover
these expenses. Write an inequality for the amount of money Kamisha must have in her account,
with M = the money in her account.
33. In a math class at a community college, only five chapter exams are given and an 80% must be
achieved in order to pass the class. Pam has completed the first four exams with scores of 71, 84,
79, and 81. Write an inequality to find the minimal score Pam can earn on the fifth exam in order
to pass the exam.
6 Level 5 34. The girls’ soccer team wants to raise $2000 to buy new goals. Write an inequality that represents the number of hot dogs and the number of sodas that they will need to sell to make their goal. 35. A curbside recycling service will remove up to 50 pounds of plastic and paper products each week. They charge $0.25 per pound of plastic and $0.75 per pound of paper products. a. Write an inequality that describes the pounds of each kind of product that can be included in the curbside service. b. Write an equation that describes the charge. 36. At a sports shop, basketballs cost $20 each, and footballs cost $18 each. You have $150 to spend on basketballs and footballs. Write an inequality to represent the possible number of basketballs and footballs you can buy. 37. You rent a car and are offered two payment options. You can pay $25 a day plus $0.15 a mile (option A) or you can pay $10 a day plus $0.40 a mile (option B). Write an inequality to model when option A will be cheaper than option B. 7