Apples cost $a per kilo, bananas cost $b per kilo, and coconuts cost $c each. Annie spends a total of $26 on 2 kilos of apples, 2 kilos of bananas, and 1 coconut. Bob spends a total of $40 on 4 kilos of apples, no bananas, and 2 coconuts. And Carol spends a total of $18 on 3 kilos of apples, 1 kilo of bananas, and no coconuts. (a) What is an equation that defines Annie's total spending as a function of a,b, and c ? What is a similar equation for Bob? Carol? 3 marks (b) Write down the system of equations from part (a) in matrix form. 2 marks (c) Solve for a,b, and c by using the adjoint method. 10 marks Apples cost $a per kilo, bananas cost $b per kilo, and coconuts cost $c each. Annie spends a total of $26 on 2 kilos of apples, 2 kilos of bananas, and 1 coconut. Bob spends a total of $40 on 4 kilos of apples, no bananas, and 2 coconuts. And Carol spends a total of $18 on 3 kilos of apples, 1 kilo of bananas, and no coconuts. (a) What is an equation that defines Annie's total spending as a function of a,b, and c ? What is a similar equation for Bob? Carol? 3 marks (b) Write down the system of equations from part (a) in matrix form. 2 marks (c) Solve for a,b, and c by using the adjoint method. 10 marks