Problem Set 9
Name:______________________
Rea, 20067
Solve at least 8 problems on a separate sheet of paper, with this sheet attached to the front as a cover sheet. Show all work in detail, and be prepared to explain what you did to the class. 1.
Tickets to a school play cost $1.50 if bought in advance, and $2.00 if bought at the door. By selling all 200 of their tickets, the players brought in $360. How many of the tickets were sold in advance?
2.
Joe was given $75 for a birthday present. This present, along with earnings from a summer job, is being set aside for a mountain bike. The job pays $6 per hour, and the bike costs $345. To be able to buy the bike, how many hours does Joe have to work?
3.
Let h be the number of hours that Joe works in the problem described in 2 (above). What quantity is represented by the expression 6h? What quantity is represented by the expression 6h + 75? a) Solve and graph the solutions to the inequality 6h + 75 > 345 on a number line. b) Solve and graph the solutions to the inequality 6h + 75 < 345 on a number line. c) What do the solutions to inequality 6h + 75 > 345 signify?
4.
Justin began a number puzzle with the words "Pick a number, add 7 to it, and double the result." Justin meant to say "Pick a number, double it and add 7 to the result." Are these two instructions equivalent? Explain.
5.
To earn a spot on a local track team, a runner must run a 5km course in less than 20 minutes. a) What is the average speed of a 20minute runner, in km per hour? in meters per second? Express your answer to two decimal places. 5 x b) One approach to this problem is to set up a proportion = . Explain the 20 60 role of 60 in this proportion. Solve the proportion.
6.
Thomas paid to have some programs printed for a football game. The printing cost was 54 cents per program, and the plan was to sell them for 75 cents each. Bad weather kept many people away from the game, however, and unlucky Thomas was left with 100 unsold copies, and lost $12 on the venture. How many programs should Thomas have printed?
7.
The Mount Major hike starts in Alton Bay, 716 feet above sea level. The summit is 1796 feet above sea level, and it takes about 45 minutes for a typical hiker to make the climb. Find the rate at which this hiker gains altitude, in feet per minute.
8.
Alison bought several pens at Walgreen's for 60 cents each. Spending the same amount of money at the Bookstore, Alison then bought a few more pens that cost 80 cents each. In all, 42 pens were bought. How many pens did Alison buy at the Bookstore?
9.
Combine over a common denominator without using a calculator: 1 1 1 1 1 1 a) = b) + c) + 4 5 10 11 x x +1 Evaluate your answer to c) with x = 4 and then with x = 10. How do these answers compare to your answers in a) and b)?
10.
Each step of the stairs leading from room 9 to room 107 in the Academy Building has a vertical rise of 7 inches and a horizontal run of 12 inches. Each step of the marble staircase leading to the Assembly Hall has a vertical rise of 5.5 inches and a horizontal run of 13 inches. Which flight of stairs is steeper? Why?