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?
Jack from Stoke by Nayland Middle School sent
in a solution to the problem that makes, in his words, "the World's
most bland cereal bar":
Anja from Stoke by Nayland Middle
School, John and Andrew from Lazonby C of E School and Esther
(school not given) managed to combine all 3 ingredients as
Esther observes that:
Taylor & Nia from Llandaff City
Church in Wales Primary School also combined the 3 ingredients, but
in a different way:
The ratio that Taylor and Nia have
worked out is:
The problem can also be defined in one
(where $a =$ weight of apricots, $n =$ weight of nuts, $s =$ weight
$$7a + 6n + 4s = 5(a + n + s)$$
$$2a+ n = s$$
Any combination that fits the relationship $s
= 2a + n$ will satisfy the criteria (see the examples above).
Notice that this is a more general solution than the ratios offered
You can now use the equation to find many more