Algebra : Estimation, Word Problems and Optimization

1. Use inductive reasoning to determine the next three numbers in the pattern: 2, 9, 20, 35...

2. Make a conjecture about the relationship between the original number and the final number in the following process.
Pick a number
Multiply the number by 12
Add 12 to the product
Divide the sum by 4
Subtract 3 from the quotient

3. Find a counterexample to the statement "The square of a number added to the sum of the number and five is a prime number"

4. Estimate: 25.78 + 240.22 + 800.36 + 4.322 + 0.9142

5. Estimate: 5982 x 7994

6. Estimate the area of the triangle in square units. Each square represents 1 square unit.

7. A small area in front of a building is triangular in shape. The perimeter of the triangle is 37 meters. The second side is one-half of the first side in length. The third side is 3 meters less than the first side. Find the length in meters of each side of the triangular region.

8. A six pack of soda costs $1.93. A carton of 24 cans costs $6.70. How much will be saved by purchasing the carton rather than 4 individual six packs?

9. Mike invested $6000 for one year. He invested part of it at 9% and the rest at 11%. At the end of the year he earned $624 in interest. How much did he invest at each rate?

10. Car rental agency A will rent a compact car for $35 per day and an additional charge of $0.24 per mile. Car rental agency B will charge only $0.16 per mile but charges $41 per day. If Adam wanted to rent a car for three days, how many miles would Adam have to drive to make car rental agency B a better bargain?

See attached file for full problem description.