In a fraction, if the numerator is increased by 2 and the denominator is decreased by 3, then the fraction becomes 1. Instead, if the numerator is decreased by 2 and denominator is increased by 3, then the fraction becomes 3/ 8. Find the fraction.

What is the volume of a cylindrical container with base radius 5 cm and height 20 cm?
 

In the x - y plane, the graph of line   has slope 3 . Line k  is parallel to line   and contains the point  ( 3, 10 ). Which of the following is an equation of line k ?

Note:
The general equation of a line is  Ax + By = c. This form is modified to give us many other forms of equation of a line which involve the use of slope, x intercept, y intercept, etc. The student needs to be familiar with all these forms of equation of a line.

The ratio of the lengths of the parallel sides of a trapezium is 3:2. The shortest distance between them is 15cm. If the area of the trapezium is 450 sq. cm. Find the sum of the lengths of the parallel sides ?

The sum of two numbers is 52 and their difference is 20. find the numbers?

A 12% brine solution was mixed with a 16% brine solution to produce a 15% brine solution. How much of the 12% brine solution and how much of the 16% brine solution were used to produce 40 L of the 15% solution?

Candies  cost $2 an ounce and have 500 calories in an ounce. Cookies cost $3 an ounce and have 400calories in an ounce. A mixture of candies and cookies costs $29 and has 4,800 calories. Create a system of equations to model this scenario. How many ounces of candies are there in the mixture?

Chocolate  costs $7 a pound. Biscuits cost $9 a pound. There is a mixture of peanuts and cashews that weighs 10pounds and costs $84. How many pounds of chocolates are there in the mixture?

A fence is put around a rectangular plot of land. The perimeter of the fence is 28 feet. Two of the opposite sides of the fence cost $10 per foot. The other two sides cost $12 per foot. If the total cost of the fence is $148, what are the dimensions of the fence?

A Stone of volume 36 cubic cm is placed in a rectangular tank measuring 8 cm by 6 cm by 5 cm. A student wants to fill the tank with water to a height of 4 cm. What is the volume of the water needed?

The area of a trapezium side field is 480sq. m , the height is 15m and one of the parallel side is 20m .Find the other side ?

The velocity v , in meters per second, of a falling object on Earth after t seconds, ignoring the effect of air resistance, is modeled by the equation v = 9.8t . There is a different linear relationship between time and velocity on Mars, as shown in the table below.

If an object dropped toward the surface of Earth has a velocity of  58.8 meters per second after t  seconds, what would be the velocity of the same object dropped toward the surface of Mars after t  seconds, ignoring the effect of air resistance?

Note:
When we get time t = 6  seconds, we can find the answer directly from the options. As 6 is between 4 and 8, and the relation is linear,
so the velocity is between 14.8 metres per second and 29.6 metres per second.

A pet store has 30 animals. Some are cats and the rest are dogs. The cats cost $50 each. The dogs cost $100each. If the total cost for all 30 animals is $1900, how many cats are there?

The parallel sides of a trapezium are 30 cm and 10 cm and the other two sides are 13 cm and 21 cm. Find its area?

A Hollow cylindrical pipe is 21 cm long. If its outer and inner diameters are 10 cm and 6 cm respectively, then find the volume of the metal used in making the pipe?

There are 8 people in the lift. Few are ladies and the rest are children. Each lady weighs 150 pounds. Each child weighs 50 pounds. The total weight of the 8 people is 800 pounds. Construct the system of linear equations and use elimination method to solve.