You may also like

problem icon

How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

problem icon

Do Unto Caesar

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?

problem icon

Oh for the Mathematics of Yesteryear

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?

Punky Fish

Stage: 3 Short Challenge Level: Challenge Level:1
Every fish has at least 8 stripes, so if we had 10 fish, there would be 80 stripes with 6 stripes not yet counted.
As a male fish has one extra stripe, these 6 stripes must belong to 6 male fish.

So there are 6 males and 4 females.

Therefore the ratio of male to female fish is 3:2.

Alternatively, if there are f females and m males then $86=8f+9m=8(f+m)+m$.
Now $86=8\times 10+6=8 \times 9+14...$
Only the first of these is feasible so m=6 and f=4.
Therefore the ratio of male to female fish is $3:2$.

This problem is taken from the UKMT Mathematical Challenges.