ratio possibly with algebra questions

some demanding ratio questions that are used or adapted from recent GCSE papers and some from the additional/further maths papers

opinions differ on how to teach approaches to these sorts of questions
all can involve algebra (a relatively unthinking and so, for me, safer way) but can also be done by considering e.g. lowest common multiples with the part (or whole) that does not change and then appropriate scaling (equivalent ratios)

the powerpoint is here

you can solve these questions by listing equivalent ratios (scaling)

and seeing which 'works'















these considerations can be sped up by considering the lcm of what does not change, in this case the number of blue beads (thanks to Richard Trimble)

a bar model might help (even if only retrospectively...)

and then consider what fraction the extra 5 must be of the original red bar

or students might prefer to use an algebraic technique

involving simultaneous equations:

or, setting up an equation and cross-multiplying:

the course AQA 8360 has involved questions like ratio (iii)

show that the second statement follows from the first