1. You are building models with tinker toys. You have 100 sticks and 65 wheels. You want to build as many cubes and pyramids as possible without any tinker toy parts left over. Each cube requires 8 wheels and 12 sticks. Each pyramid requires 5 wheels and 8 sticks. How many cubes and how many pyramids can you build?
2. When I visited Massachusetts during the summer, my plane ticket listed the following scheduled departure and arrival times:
|
Minneapolis to Boston |
leave 9:35am |
arrive 1:18pm |
|
Boston to Minneapolis |
leave 1:25pm |
arrive 3:25pm |
Assuming that Boston is 1800 miles from Minneapolis and that the plane travelled at the same speed in each direction, what was the plane's speed and the wind speed? Note that all times are local times! Boston is in the eastern time zone!
3. A biologist estimates that the region she is studying can supply 60,000 kg of food for birds during the nesting season. The region has an area of 150,000 m2. Two species of birds inhabit the region and compete for food and territory. Each nesting pair of species A needs 33 kg of food and has a territory of 100 m2. Each nesting pair of species B needs 58 kg of food and has a territory of 75 m2. How many nesting pairs of each species can the area support?
4. A diet is to contain 16 units of carbohydrates and 20 units of protein. Food A contains 2 units of carbohydrates and 4 units of protein. Food B contains 2 units of carbohydrates and 1 unit of protein. How many units of each food should be purchased to meet these requirements?
Food A costs $1.20 per unit and food B costs $0.80 per unit. What is the cost of this amount of food?
5. The EMCA Cement Company has an old plant it wishes to continue running. To be profitable, annual production must be at least 2,500,000 barrels of cement. Government regulations require that total dust emissions not exceed 800,000 lbs per year.
The plant has two electrostatic dust collectors. Collector A allows 0.5 lbs of dust and costs $0.20 per barrel. Collector B allows 0.2 lbs of dust but costs $0.25 per barrel. Determine the amount of cement that should be produced using each collector. What is the total cost to produce the cement?