Issy goes to buy some fruit. She has been told by one friend that 2 apples and 3 bananas costs £3.80. She has been told by another friend that 5 apples and a banana costs £3.65. what are the individual costs of an apple and a banana?

To solve this we form two simultaneous equations. To make things easier lets denote apples as A and bananas as B. So this means we can write the above information in two equations like so: EQ1) 2A + 3B = 380p EQ2) 5A + B = 365p To solve we will need to eliminate one of the values, either A or B. This can be achieved by subtracting 3 multiples of EQ2 from EQ1 to obtain: -13A = -715 Then solve this to find A, A = -715/-13 = 55p So one apple costs 55p. We can use this information to find the price of a banana by subbing it back into either equation. EQ2 is easier. So EQ2 becomes: (5 x 55p) + B = 365p simple rearrangement will then give B to be:B = 365p - 275p = 90p Answer: Apples cost 55p, Bananas cost 90p (note there a several other ways to obtain the same answer)