The problem describes a school courtyard that is 600 $m^2$. A fraction, $\frac{2}{5}$, of the courtyard is a flower bed, and 150 $m^2$ of the remaining area is lawn. We are asked to find: (1) The area of the flower bed in $m^2$. (2) The ratio of the area of the flower bed to the area of the lawn.

1. Problem Description

The problem describes a school courtyard that is 600 $m^2$. A fraction, $\frac{2}{5}$, of the courtyard is a flower bed, and 150 $m^2$ of the remaining area is lawn.

We are asked to find:

(1) The area of the flower bed in $m^2$.

(2) The ratio of the area of the flower bed to the area of the lawn.

2. Solution Steps

(1) Area of the flower bed:

The courtyard is 600 $m^2$.

The fraction of the courtyard that is a flower bed is $\frac{2}{5}$.

Therefore, the area of the flower bed is $\frac{2}{5}$ of 600 $m^2$.

Area of flower bed = $\frac{2}{5} \times 600$

Area of flower bed = $2 \times \frac{600}{5}$

Area of flower bed = $2 \times 120$

Area of flower bed = $240$ $m^2$

(2) Ratio of flower bed area to lawn area:

The area of the flower bed is 240 $m^2$.

The area of the lawn is 150 $m^2$.

Ratio = $\frac{\text{Area of flower bed}}{\text{Area of lawn}}$

Ratio = $\frac{240}{150}$

Ratio = $\frac{24}{15}$

Ratio = $\frac{8}{5}$

Ratio = $1.6$

3. Final Answer

(1) The area of the flower bed is 240 $m^2$.

(2) The flower bed's area is 1.6 times the lawn's area.