Lottie has a bag of applies. She gives half of them to Fred. Fred eats two and then has four left. How many apples did Lottie have at the start?

General method
1.     Write the information down in equation form defining unique symbols to represent the unknowns2.     DOF analysis: Count the number of equations and unknowns? a.     If #E = #U → unique solution b.     If #E > #U → No solutions c.     If #E > #U → Inf. many solution (unknowns can take any value)3.     If a) applies a.     Solve the problem to find the value of the unknowns4.     Check your answer a.     Substitute the value of the unknowns back into all the equations. If the equations still hold (i.e. LHS = RHS), then the solution is unique. b.     If not → repeat step 3 or check if the equations are written correctly in step 1.
Solution for example question
Step 1·       L = Lottie; F = Fred·       “Lottie has a bag of applies. She gives half of them to Fred.” → F = L/2 (Eqn. 1)·       “Fred eats two and then has four left” → F -2 = 4 (Eqn. 2)
Step 2·       DOF check: #E = 2 and #U = 2 → unique solution
Step 3·       Use Eqn.2 → F = 4 + 2 = 6·       Substitute into Eqn.1 → F = L/2 → 2F = L → L = 2 x 6 = 12
Step 4·       If L = 12 → F = 12/2 = 6 ·       F – 2 = 6 – 2 = 4 ·       The solution is correct.