algebra

If x varies directly as y and inversely as z, and \(x=14\) when \(y=7\) and \(z=2\), find the value of x when \(y=16\) and \(z=4\).

The electric power which a transmission line can transmit is proportional to the product of its design voltage and current capacity, and inversely to the transmission distance. A 115-kilovolt line rated at 100 amperes can transmit 150 megawatts over 150 km. How much power, in megawatts can a 230 kilovolt line rated at 150 amperes transmit over 100 km?

The time required for an elevator to lift a weight varies directly with the weight and the distance through which it is to be lifted and inversely as the power of the motor. If it takes 30 seconds for a 10 hp motor to lift 100 lbs through 50 feet, what size of motor is required to lift 800 lbs in 40 seconds through 40 feet?

The selling price of a TV set is double that of its cost. If the TV set was sold to a customer at a profit of \(25\%\) of the net cost, how much discount was given to the customer?

A group of EE examinees decided to hire a mathematics tutor from Excel Review Center and planned to contribute equal amount for the tutor's fee. If there were 10 more examinees, each would have paid P 2 less. However, if there were 5 less examinees, each would have paid P 2 more. How many examinees are there in the group?

A bookstore purchased a best selling price book at P 200.00 per copy. At what price should this book be sold so that, giving a \(20\%\) discount, the profit is \(30\%\)?

Jojo bought a second hand Betamax VCR and then sold it to Rudy at a profit of \(40\%\). Rudy then sold the VCR to Noel at a profit of \(20\%\). If Noel paid P 2,856 more than it cost to Jojo, how much did Jojo paid for the unit?

In a certain community of 1,200 people, \(60\%\) are literate. Of the males, \(50\%\) are literate and of the females \(70\%\) are literate. What is the female population?

A merchant has three items on sale, namely a radio for P 50, a clock for P 30 and a flashlight for P 1. At the end of the day, he sold a total of 100 of the three items and has taken exactly P 1,000 on the total sales. How many radios did he sale?

The arithmetic mean of a and b is

The sum of three arithmetic means between 34 and 42 is

Gravity causes a body to fall 16.1 ft in the first second, 48.3 in the \(2^{nd}\) second, 80.5 in the \(3^{rd}\) second. How far did the body fall during the \(10^{th}\) second?

If the first term of an arithmetic progression is 25 and the fourth term is 13, what is the third term?

Find the \(30^{th}\) term of the arithmetic progression 4, 7, 10,...

How many terms of the progression 3, 5, 7, ... must be taken in order that their sum will be 2600?

In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there?

What is the sum of the progression 4, 9, 14, 19... up to the \(20^{th}\) term?

A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer, and so on until there are 10 bricks in the last layer. How many bricks are there all together?

Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35.

A besiege fortress is held by 5700 men who have provisions for 66 days. If the garisson losses 20 men each day, for how many days can the provision hold out?