Punky fish
A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?
Age
14 to 16
Challenge level
Problem
A male punky fish has 9 stripes and a female punky fish has 8 stripes.
I count 86 stripes on the fish in my tank.
What is the ratio of male fish to female fish?
If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: male:female is 3:2
Starting with females
Every fish has at least 8 stripes
10 fish with 8 stripes have 80 stripes
There are 6 more stripes
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.
Starting with males
Now $86=9\times9 + 5$
$=9\times 8+9+5 = 9\times8+14$
$=9\times 7+18+5 = 9\times7+23$
$=9\times 6+27+5 = 9\times6+32=9\times6+8\times 4$
Therefore the ratio of male to female fish is $3:2$.