Challenge Level

We had just a few solutions sent in for this task.

Monty from the British School in Brussels in Belgium said:

I decided to use the grid mode and count the squares in order to work out the ratios. Here are some of my answers:

Gianna, also from the International School of Brussels in Belgium sent in this good piece of work:

Well done also to Isis (South Island School), Rohaan (Long Bay Primary) and Samantha (The Hamlin School) for completing this task! Samantha explained how she manged to find a pair with the same ratio as the yellow and pink rods:

The pink rod had 4 units and the yellow one had 5 units. This meant that they had a ratio of 4:5. I then needed to find a like ratio. This can be done by multiplying both numbers in the ratio by the same number. In this case the number had to be 2 because the longest rod is 10 units. So the 8 (brown coloured) and the 10 (orange coloured) rods would have the same ratio as the 4 (pink coloured) and
the 5 (yellow coloured).

She also found pairs with the same ratio as the combined yellow+orange to blue:

The ratio of yellow (5) + orange (10) to blue (9) is equal to the ratio 15 to 9. This ratio can be simplified to a 5:3 ratio by dividing both 15 and 9 by 3. Therefore, the **yellow and green rods** form an equal ratio to that of the yellow + orange to the blue. Another equal ratio would be 10 to 6. Therefore, the **dark green
and orange rods** also form an equal ratio.

Finally she noted that the rods with the same ratio as 9:6 have already been given!

The ratio of 9:6 can be simplified to the ratio 3:2. The possible combinations with rods for that ratios are shown at the start of the question!

Thank you to all those who sent in their work, thoughts and ideas.