Practice translating sentences into equations

Transcription

1 Algebra 1 (2) Ms. Young 27 January 2011 WS #1 Word problems using systems of equations A. Some preliminary work for word problems Practice translating sentences into equations a. x is four more than y. (x equals 4 more than y) b. The sum of A and B is fifty-six. c. y is twice as big as x. (y equals two times x) d. P is 6 less than Q Practice translating phrases into algebraic expressions (not equations) e. The value (total cost) of B bananas at $3 each f. The value of x tickets at $2.50 each. g. The cost of three muffins that cost $M each. h. The number of total points 12 questions are worth if each question is worth P points. B. Our first systems word problems! 1. The sum of two numbers is 52. The difference of the same two numbers is 20. Find the numbers. Let x = first number Let y = second number Equations:

2 2. One number is 5 more than a second number. The sum of the two numbers is 115. What are the numbers? Let x = first number Let y = second number 3. One number is 5 more than 3 times a second number. The larger number decreased by the smaller number is 29. Find the numbers. Let x = smaller number Let y = larger number The next problems are a little more complicated. We ll do the first two together. Requirements: Circle all of the numbers in the problem. If the variables are not already stated, write a let statement naming your two variables. Write two equations involving your two variables. Solve using either substitution or linear combination. Circle and label your answers. Check your answers.

3 4. Tickets to see the school play cost $2.50 for students and $4.00 for adults. The school sold a total of 850 tickets, taking in $2395. How many adult tickets were sold? How many student tickets were sold? Let S = number of student tickets sold Let T = number of adult tickets sold 5. Two hungry football players go through the cafeteria line. One orders 3 slices of lasagna and 3 salads and pays $8.64. The other orders 4 slices of lasagna and 2 salads and pays $9.54. How much is one slice of lasagna? How much is one salad? Let L = cost of one slice of lasagna Let S = cost of one salad 6. If the final exam has fifteen multiple choice problems and twelve long answers, it would be worth 90 points. If it had twenty-five multiple choice problems and ten long answers, it would be worth 100 points. How many points is one multiple choice problem worth? How many points is one long answer problem worth? Let x = number of points for each MC question Let y =

4 Algebra 1 (2), Ms. Young 27 January 2011 Section 7.4 in the book CLASS PRACTICE -- Word problems using systems of equations 1. Five deluxe pizzas and six standard pizzas cost $102. Six deluxe pizzas and twelve standard pizzas cost $156. How much does one deluxe pizza cost? How much does one standard pizza cost? Let x = cost of Let y = cost of 2. Five gallons of regular unleaded gas and eight gallons of premium gas cost $ Five gallons of regular unleaded and two gallons of premium cost $8.75. Find the cost of each kind of gasoline. Let x = cost of Let y = cost of 3. The difference between two numbers is 4. Three times the larger number minus five times the smaller number equals 2. Find the numbers. Let x = smaller number Let y = larger number

5 4. Four cookies and three milks cost $5.05. Three cookies and two milks cost $3.65. How much does one cookie cost? How much does one milk cost? Let x = cost of one cookie Let y = cost of 5. Airline fares for flights from Tifton to Adel are $300 for first class and $250 for coach class. A flight had a total of 52 passengers who paid a total of $13600, how many of each type of passenger was on the trip? Let x = number of first class passengers Let y = number of 6. Tickets for the bleachers cost $12, and for the third base line cost $32, Eighteen tickets were sold, worth a total of $476. How many of each ticket was sold? Let x = number of bleacher seats sold Let y = number of