Write the following problem as a pair of simultaneous equations and solve:
a) find two numbers whose difference is 5 and whose sum is 23.
b) a rectangular house has a total perimeter of 34 metres and the width is 5 metres less than the length. what are the dimensions of the house?
c) if two chupa chups and three wizz fizzes cost $2.55, but 5 chupa chups and seven wizz fizzes cost $6.10, find the price of each type of lolly.