# Problem of the Week ## Potato Planting

Vince plans to plant his potatoes in a rectangular array.

The potatoes need to be at least 25 cm apart and at least 50 cm from the brick edges of the garden bed.

The garden bed is 2 metres wide and 6 metres long.

What is the greatest number of potatoes he can plant?

Below is a drawing of the garden bed. The potatoes are planted in a grid of rows (horizontal) and columns (vertical)

Potatoes in one row

For the potatoes to be at least 50 cm from the edges, the maximum distance of the first potato in a row to the last one in a row

= 600 cm – (2 x 50) cm

= 500 cm

The potatoes must be at least 25 cm apart, so the number of intervals between the potatoes in one row

= 500 cm ÷ 25 cm

= 20

There are 20 intervals between potatoes, so there must be 20 + 1 = 21 potatoes in each row.

Potatoes in one column

For the potatoes to be at least 50 cm from the edges, the maximum distance of the first potato in a column to the last one in a column

= 200 cm – (2 x 50) cm

= 100 cm

The potatoes must be at least 25 cm apart, so the number of intervals between the potatoes in one column

= 100 cm ÷ 25 cm

= 4

There are 4 intervals between potatoes, so there must be 4 + 1 = 5 potatoes in each column.

The total number of potatoes in the array is the number in each row times the number in each column.

21 x 5 = 105 potatoes that Vince can plant.