Mr. Dan

An Edgehill University maths problem!

 Team

Helen, Jade, Shivani, Pualina and Dan

The question:

Katie has started a new job as a primary school teacher. Asparts of a science experiment, she helped 30 of her pupils to plant a seed each. After one week the class measured their plants’ heights and noted them to the nearest centimetre. Several of the class’ plants had grown to 5cm. A smaller number had grown to 2cm. The rest, including Micky’s, had only grown 1cm.  The class added up the heights of all the plants. After another week they measured again. All the plants except one had doubkled in size. Poor Micky’s was still 1cm. The class then added uo the total heights of their plants which came to 131cm. How many plants of each height were there after one week?

  How we solved it:

We analysed the question thoroughly and came to the conclusion that only Micky’s plant remained 1cm. Some plants were 1cm the first week, then grew to 2cm. Some were 2cm the first week, than grew to 4cm. The rest were 5cm the first week, and so were 10cm the next week. 

If the plants’ total was 131cm after two weeks, than they was 130cm without Micky’s. Therefore, during the first week, the combined total of the heights of the plants was 66cm.

If we took off the value of Micky’s plant, we were left with 65cm. We knew we had to make this figure using 5’s, 2’s and 1’s. And we could only use 29 numbers (since there were 30 in the class, and we already knew about Micky). After some elaborate trial, error, and improvement using an Microsoft Excel document (to check they were accurate), we came to this conclusion.

8 plants were 5cm

5 plants were 2cm

16 plants(includine Micky’s) were 1cm

Checking:

We can check if this answer is correct by doubling all the values. If the result equals 132, than we are corret!

8 X 5=40

5 X 2 = 10

16 X 1 = 16

66 X 2  132

Congratulations! GO SIGFIGS!