If the sides of the triangle in the diagram are 3, 4 and 5, what is
the area of the shaded square?
At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?
A garrison of 600 men has just enough bread ... but, with the news
that the enemy was planning an attack... How many ounces of bread a
day must each man in the garrison be allowed, to hold out 45 days
against the siege of the enemy?
We received several incorrect solutions
like the ones below:
Combining paints A ($1:4$) and
They are based on the misconception that you
can add the ratios to work out the necessary combinations. The
solutions given have assumed that the 'parts' in the ratios are of
equal size so that a can in the ratio $1:3$ contains half the
amount of the one in the ratio $1:7$.
However, one can of paint C and one can of paint D does
not produce paint
in the ratio $2:10$ (or $1:5$), since that would assume that the
one part red in can C has the same volume as the one part red in
This can't be the case since there are $4$ parts in can C and $8$
parts in can D,
so $1/4$ of can C is red and $1/8$ of can D is red.
To compare equal quantities we will need to express the ratio of
the colours in can C as $2:6$, so we have:
in can C: $2/8$ red and $6/8$ white
in can D: $1/8$ red and $7/8$ white
Combining one can of each paint will now give us
$3/8$ red and $13/8$ white,
that is, paint in the ratio $3:13$
Andy from Clitheroe Royal Grammar School sent us his work on this