Algebra
Criteria A: Knowing and Understanding
Maximum: 8
Objective:
i. select appropriate mathematics when solving problems in both familiar and unfamiliar situations
ii. apply the selected mathematics successfully when solving problems
iii. solve problems correctly in a variety of contexts.
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Translation of verbal statements into algebraic expression
Continuation from Set-1
21. half a number less three.
22. triple a number plus four is divided by two.
23. a number less ten is doubled.
24. seven subtracted from eight times a number.
25. one-third a number times two.26. three times the sum of a number and 4
27. the sum of a number and 8 subtracted from 30
For questions 28 through 30, let x the distance traveled by Nick. Translate each English phrase into an algebraic statement.
28. Annie drove 7 miles less than the distance traveled by Nick.
29. Wayne traveled 8 miles further than the distance traveled by Nick.
30. Karl swam seven-eighths of the distance traveled by Nick.
31. The perimeter of a square patio is 48 feet. What are the dimensions of the patio?
32. The length of a rectangle is six feet greater than the width. the perimeter is 168 feet. What are the dimensions of the rectangle?
33. The length of a rectangle is 1 yard more than twice the width. The perimeter is 218 yards. What is the length and the width?
34. The width of a rectangle is 3 meters more than half of the length. the perimeter is 516 meters. What is the length and the width?
35. The perimeter of a triangle is 35 cm. The length of the third side is twice the length of the first side. The length of the second side is half the length of the first side. Find the lengths of the three sides.
36. The shortest side of a triangle is 8 mm less than the length of the middle side. The longest side of the triangle is 10 mm more than the length of the middle side. If the perimeter of the triangle is 29 mm, find the length of each side.
37. The town of Mathville is triangular in shape and has a perimeter of 104 km. The interstate borders the southern part of the town, but town residents want to build two more roads, one on each side of the town. The length of one side of the town is 1/2 the length of the interstate. The length of the other side is 2/3 the length of the interstate. Determine the length of road necessary to complete the town’s task. That is, determine the length of each of the two sides of the town not bordered by the interstate. HINT: Draw a picture.
38. The perimeter of a trapezoid is 33 meters. The length of the left and right sides are the same. See the figure below. If the length of the top is 6 meters more than a side and the length of the bottom is 11 meters more than the length of a side. Find the length of each side, the top and the bottom.
39. The perimeter of a trapezoid is 14 inches. The length of the left and right sides are the same. If the length of the bottom is twice the length of a side and the length of the top is 1 inch less than the length of a side. Find the length of each side, the top and the bottom.
More problems:
40. Tia flew from Logan Airport (in Boston) to SeaTac Airport (in Seattle), a distance of approximately 2500 miles. Her flight has a layover in Pittsburgh. The distance from Boston to Pittsburgh is about a quarter the distance between Pittsburgh and Seattle. How far is it between cities?
41. The total distance flown from NY’s JFK airport to Moscow, Russia is 5015 miles. A typical flight goes from NY to Toronto, Canada, to Helsinki, Finland, to Moscow. The distance from NY to Toronto is 347 miles. The distance from Toronto to Helsinki is 3552 miles more than the distance from Helsinki to Moscow. What is the distance between Toronto and Helsinki, and what is the distance between Helsinki and Moscow? HINT: See diagram below.
42. While planning a vacation to Europe, Cal wanted to go to Dublin, Ireland, London, England and Paris, France. The distance from Dublin to London is 78 more miles than the distance between London and Paris. If the distance between Dublin and Paris is 504 miles, including the stop in London, what is the distance between London and Paris? What is the distance between Dublin and London? HINT: Draw a diagram like the one in problem 41.
43. The only available flight from Logan Airport to Denver, Colorado must stop in Chicago. The distance between Boston and Chicago is 55 miles less than the distance between Chicago and Denver. The total distance flown from Boston to Chicago to Denver is 1767 miles. Find the distance between Boston and Chicago, and between Chicago and Denver.
44. Dan has 12 feet of rope. He plans on making 2 jump ropes. If the length of the longer piece is 2 feet longer than the shorter piece, how long are the two jump ropes going to be?
c Fixed Rate + Variable Rate = Total Rate
45. Zip-Plus is a company that adds bar codes to US Mail. They charge $100 for the first 500 pieces of mail and $0.10 for each additional piece. If a company’s total bill for bar coding was $143.20, how many pieces of mail were bar coded?
46. A rookie baseball player had a clause in his contract that paid him $175,000 a year plus $200 per hit. If his salary last season was $199,000, how many hits did he receive last season?
47. Mr. Yang’s ISP (Internet Service Provider) charges are $10 a month for 8 hours of service plus $0.50 an hour for each hour over the initial 8 hours. If his ISP bill last month was $18.50, how many hours did he spend on-line?
48. Schroder has a job as a piano player in a local nightclub. His salary consists of $175 a week plus $1.50 for each paid admission. His paycheck last week was for $340. How many paid admissions did the club have last week?
49. Brady rented a car for two days at $25 a day plus $0.15 per mile. If his total bill came to $102.50, how many miles did Brady drive?
50. Tino pays $725 a month for rent, $40 for cable and $3.60 an hour for local telephone service. If his total monthly expenditures last month were $826.20, how much time did he spend on the phone?