ALGEBRA

 ALGEBRA SET OF PROBLEMS

PROBLEM 1: Find the 30th term of the arithmetic progression 4, 7, 10,...

PROBLEM 2: A man piles 150 logs in layers so that the top layer contains 3 logs and each lower layer has one more log than the layer above. How many logs are there in the lowest layer?

PROBLEM 3: A well driller charges P100 for the first 50 ft and P10 less for every 50 ft. there after. How much would a 350-ft deep well cost?

PROBLEM 4: The arithmetic mean of six numbers is 17. If two numbers are added to the progression, the new set of numbers will have an arithmetic mean of 19. What are the two numbers if their difference is 4.

PROBLEM 5: The sum of two numbers is 4 and the product of these same numbers is 5. Find the sum of their reciprocals.

PROBLEM 6: One-half of Angela’s age two years from now plus one-third of her age three years ago is 20 years. How old is she now?

PROBLEM 7: Mr. Cruz bought a television set on an installment basis. He paid 1/3 of the cost as a down payment. After paying 2800 more, he was told that the balance was still 1/5 of the original cost. What was the total cost of his television set?

PROBLEM 8: Two guys were working on a car. One can complete the given job in six hours, but the second guy takes eight hours. They worked together for two hours, but then the first guy left to help another mechanic on a different job. How long will it take the second guy to finish the car?

PROBLEM 9: Working alone, Maria can complete a task in 100 min. Gina can complete the same task in 2 hrs. They work together for 30 minutes when Angela, the new employee, joins and begins helping. They finish the task 20 min. later. How long would it take Angela to complete the task alone?

PROBLEM 10: A pipe can fill up the tank with the drain open in three hours. If the pipe runs with the drain open for 1 hr and then the drain is closed, it will take 45 more minutes for the pipe to fill up the tank. If the drain will be closed right at the start of filling, how long will the pipe be able to fill up the tank?

PROBLEM 11: How many liters of 10% and 20% alcohol solution must be added to obtain 10 liters of 12% alcohol solution?

PROBLEM 12: Find the middle term in the expansion of (x^2 − 2y)^10.

PROBLEM 13:  In the expansion of (x^2 − 1/x^3 )^30, find the constant term.

PROBLEM 14: Find the value of MCMXCIV.

PROBLEM 15: How many minutes after 2 o’clock will the minute hand and the hour hand of a clock be in the opposite direction for the first time.

PROBLEM 16: At what time after 12:00 noon will the hour hand and minute hand of a clock first form an angle of 120 degrees?

PROBLEM 17: The growth of a colony of bacteria is given by Q = Qo e ^0.195t. If there are 500 bacteria present and t is given in hours, determine each of the following. 

a.) How many bacteria are there after half of a day. 

b.) How long will it take before there are 10000 bacteria in the colony