Flora the florist
Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?
Age
14 to 16
Challenge level
Problem
Flora the florist has $24$ white, $42$ red and $36$ yellow roses.
What is the greatest number of identical bunches she can make that uses all of the flowers?
Student Solutions
Answer: 6
Using the highest common factor
The number of bunches must divide the number of white roses, the number of yellow roses and the number of red roses.
The highest common factor of $24$, $36$ and $42$ is $6$, so the most bunches Flora can make is $6$, each consisting of $4$ white, $6$ yellow and $7$ red roses.
Using ratio
Use all the roses to make identical bunches - so all bunches will have the same ratio of colours as the total
$24:42:36$
$12:21:18$
$4:7:6$
Cannot simplify further so each bunch has $4$ white roses
So Flora can make $6$ from $24$ white roses