The number of tablets given to a patient was found to be directly proportional to the weight of the patient. If a patient with 36 kg was given 9 tablets, find how many tablets would be given to a patient whose weight is 48 kg.

  Four people can eat 2 bags of rice each weighing 10 kg in 12 days. How many people can eat 6 bags of rice of the same weight in 18 days?

The variable v varies directly as the square of x and inversely as y. Find v when x = 5 and y = 2 ? given that when v = 18 and x = 3 the value of y = 4 .

The temperature (T_i) inside a house is directly proportional to the temperature (T_o) outside the house and is inversely proportional to the thickness (t) of the house wall. If T_i = 32°C when T_o = 24°C and t = 9cm , find the value of t when T_i = 36°C and T_o = 18°C

The mass (M) which can be supported by a beam varies directly with the breadth (b) and inversely with the length (l). If a beam of breadth 2 m and length 15 m can support a mass of 200 kg, what mass can be supported by a beam which is 3 m broad and 20 m long?

If y varies inversely as and x is multiplied by n. What is the ratio of the first y to the second y?

The headmaster has enough food to last for his 600 students for 20 days from tomorrow. If 120 students leave the school today for UMISSETA game, how long will the food last?

The compression I of spring is directly proportional to the thrust, T exerted on it. If the thrust of 4N produces a compression of 0.8 cm, find:

(i) The compression when the thrust is 5 N

(ii) The thrust when the compression is 0.5 cm

The compression l of a spring is directly proportional to the thrust, T newtons exerted on it. If a thrust of 2 newtons produces a compression of 0.4cm, find:

(i) The compression when the thrust is 5 newtons,

(ii) The thrust when the compression is 0.7cm.

A shopkeeper invested sh 4,800,000 for 5 years. If the amount of money accumulated is sh 7,730,450, calculate the compound interest rate.

A bus travels 240km using 16 litres of diesel. How many litres of diesel are needed to drive 90km?

If y² varies directly to x ? 1 and inversely to x + d and if x = 2 , d = 4 for y = 1, then find x when y = 2 and d = 1.

The power(P) used in an electric circuit is directly proportional to the square of the current (I).

When the current is 8 Ampere (A), the power used is 640 Watts (W).

(i) write down the equation relating the power (P) and the current (I).

The number of square tiles needed to surface the floor of a hall varies inversely as the square of the length of a side of the tile used. If 2016 tiles of side 0.4m would be needed to surface the floor of a certain hall, how many tiles of side 0.3m would be required?

If y² varies directly as x-1 and inversely as x+d and if x=2, d=4 for y=1, then find x when y=2 and d=1.

If 8 students in a typing pool can type 210 pages in 3 days, how many students will be needed to type 700 pages in 2 days?

Juma bought motor vehicle spare parts from Japan worth 5,900,000 Japanese Yen. When he arrived in Tanzania he was charged custom duty of 25% on the spare parts. If the exchange rates were as follows:

1 US dollar = 118 Japanese Yen

1 US dollar = 76 Tanzania Shillings

Calculate the duty he paid in Tanzania shillings.

The distance of the horizon d km varies as the square root of the height h m of the observer above sea level. An observer at a height of 100m above sea level sees the horizon at a distance of 35.7 km.

Find 

(i) the distance of the horizon from an observer 70m above sea level. 

(ii) an equation connecting d and h. (6 marks)

The variables t and z in the following table are related by the formula z = atⁿ where a is a constant and n is a positive integer.

(i)Use the data from the table to determine the values of a and n.

(ii)Use the values of a and n obtained in part (a) (i) to complete the following table

If v varies directly as the square of  x and inversely as   , given that v =18 when x = 3 and y =16 , find the value of v when x = 5 and y = 4.

A shopkeeper invested sh 4,800,000 for 5 years. If the amount of money accumulated is sh 7,730,450, calculate the compound interest rate.

A dealer sells mattresses whose cost price (C) is directly proportional to the selling price(s). If the selling price and the cost price of one mattress are Tsh. 20,000 and Tsh. 18,000, respectively, find the constant of proportionality

(ii) By using the answer obtained in part (b)(i), determine the equation that relates the cost price and the selling price.

 A gardener has found that the time t to cut the grass on a square field varies directly as the square of its length (L) and inversely as the number of men (m) doing that job. If 5 men cut grass on a field of side 50 m in 3 hours, how many more men are required to cut grass on a field of side 100 m in 5 hours? Assume that the men are working on the same pace.

   The energy (E) stored in an elastic band varies as the square of the extension (x). When the elastic band is extended by 4 cm, the energy stored is 240 joules. What is the energy stored when the extension is 6 cm? What is the extension when the stored energy is 60 joules? 

In the preparation of fanta orange drink, a bottling filling machine can fill 1,500 bottles in 45 minutes. How many bottles will it fill in 4  hours?

  If X varies directly as Y and inversely as W, find the values of a and b in the table below.