2001 SMT/Algebra Problems
Contents
[hide]Problem 1
Find the result of adding seven to the result of forty divided by one-half.
Problem 2
Each valve , , and , when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves and open it takes 1.5 hours, and with only valves and open it takes 2 hours. How many hours will it take to fill the tank with only valves and open?
Problem 3
Julie has a 12 foot by 20 foot garden. She wants to put fencing around it to keep out the neighbour’s dog. Normal fenceposts cost 2 each while strong ones cost 3 each. If Julie needs one fencepost for every 2 feet and has 70 to spend on fenceposts, what is the greatest number of strong fenceposts she can buy?
Problem 4
is a real polynomial of degree at most 3. Suppose there are four distinct solutions to the equation = 7. What is ?
Problem 5
Let be defined by . What is ?
Problem 6
If for three distinct positive numbers , , and , Then find the numerical value of .
Problem 7
If and , find
Problem 8
Determine the value of
Problem 9
Find all solutions to
Problem 10
Suppose , , satisfy Find