A factory produces 2 types of component a and b. The profit for each component of type a is £3.50 and of type b is £6.50. In a given week 1,440 components are sold making a total profit of £6 840. How many components of each type were sold in that week?

This is just a small system of equations with two unknowns.

a+b=1440... number produced

3.5a+6.5b=6840... total profit.

Solve for a and b.