Roses were planted 100 cm apart around a rectangular garden. There were no roses at the corners. They started 1 m from each corner. The garden was 5 m by 3 m. How many roses were planted?

For a side of n meters, n-2 meters have roses, so there are 10(n-2)+1 roses.

total roses: 2(10(5-2)+1 + 10(3-1)+1) = 104

To find the number of roses planted, we need to determine the number of gaps between the roses along each side of the garden.

Let's start with the longer side of the garden, which is 5 meters. Since there are no roses at the corners, we subtract 1 meter from each end, leaving us with a distance of 5 - 1 - 1 = 3 meters between the roses.

Since the roses were planted 100 cm apart, we convert the distance between the roses to centimeters: 3 meters = 300 cm.

Next, we calculate the number of gaps between the roses on the longer side by dividing the distance between the roses by the gap size: 300 cm / 100 cm = 3 gaps.

Now, let's move on to the shorter side of the garden, which is 3 meters. Similarly, we subtract 1 meter from each end, resulting in a distance of 3 - 1 - 1 = 1 meter between the roses.

Converting the distance between the roses to centimeters gives us: 1 meter = 100 cm.

We calculate the number of gaps between the roses on the shorter side by dividing the distance between the roses by the gap size: 100 cm / 100 cm = 1 gap.

To find the total number of roses, we multiply the number of gaps on both sides: 3 gaps (longer side) * 1 gap (shorter side) = 3 roses.

Therefore, a total of 3 roses were planted around the rectangular garden.