(a) Solve the equation : \(\frac{2}{3}(3x - 5) - \frac{3}{5}(2x - 3) = 3\)

(b) 

In the diagram, < STQ = m, < TUQ = 80°, < UPQ = r, < PQU = n and < RQT = 88°. Find the value of (m + n).

(a) The angle of depression of a point P on the ground from the top T of a building is 23.6°. If the distance from P to the foot of the building is 50m, calculate, correct to the nearest metre, the height if the building.

(b) 

In the diagram, \(PT // SU, QS // TR, /SR/ = 6cm\) and \(/RU/ = 10 cm\). If the area of \(\Delta TRU = 45 cm^{2}\), calculate the area of the trapezium QTUS.

If the sixth term of an Arithmetic Progression (A.P) is 37 and the sum of the first six terms is 147, find the 

(a) first term; 

(b) sum of the first fifteen terms. 

Out of 120 customers in a shop, 45 bought both bags and shoes. If all the customers bought either bags or shoes and 11 more customers bought shoes than bags:

(a) Illustrate the this information in a diagram;

(b) find the number of customers who bought shoes;

(c) calculate the probability that a customer selected at random bought bags.

(a) A manufacturing company requires 3 hours of direct labour to process N87.00 worth of raw materials. If the company uses N30,450.00 worth of raw materials, what amount should it budget at N18.25 per hour?

(b) An investor invested Nx in bank M at the rate of 6% simple interest per annum and Ny in bank N at the rate of 8% simple interest per annum. If a total of N8,000,000.00 was invested in the two banks and the investor received a total of N2,320,000.00 as interest from the two banks after 4 years, calculate the:

(i) values of x and y

(ii) interest paid by the second bank.