Concept : grouping , common multiple.

What is important : The distance between the two walls is unchanged.

1 flag's length/spacing = 15cm
1 photo's string length/spacing = 9cm


Flags : 15cm × 3 = 45cm
Photos : 9cm × 5 = 45cm

This is the lowest common multiple.

So 3 flags take up the same length/spacing as 5 photos.

This is for one group.
In one group, there are 2 more photos than flags. (5 - 3 = 2)


Next,

In total there are 19 more photos than flags. They take the same total spacing/length.

To find the number of such groups, we would divide the total difference by the difference for 1 group.

But 19 is not exactly divisible by 2.


Why only 19 more photos? Notice that at the end of the walls , there is a spacing but there is no photo.

For example,

If there are 100 spaces, there will only be 99 photos.
If there are 3 spaces, there will only be 2 photos.


So we need to add 1 to 19 to find the actual number of spacings the photos take up.

19 + 1 = 20

Then, 20 ÷ 2 = 10

So there are 10 such groups.


Length of the wall = 10 × 45cm = 450cm