Question: How tall is the crow?
210 cm
150 cm
Graph/shape description: In the top-left, a crow sits on a post with a vertical measurement arrow labeled $210$ cm from the ground to the top of the crow. In the upper center-right, a second vertical arrow labeled $150$ cm measures from the top of the post down to the top of a crow standing on the ground. In the bottom-right, a crow on the ground has a red question mark with a short vertical arrow indicating the crow’s height. How tall is the crow?
$210$ cm
$150$ cm
?
Graph/shape description: Left side shows a crow perched on top of a pole with a vertical arrow from the ground to the crow’s head labeled $210$ cm, and the position hint is top-left. Right side shows a pole with a vertical arrow from the top of the pole down to the top of a crow standing on the ground labeled $150$ cm, and the position hint is center. At the bottom-right, a crow standing on the ground has a red question mark next to a short vertical arrow indicating the crow’s height, and the position hint is bottom-right.
1. **Problem Statement:** We need to find the height of the crow standing on the ground.
2. **Given:**
- Height from ground to top of crow sitting on post = $210$ cm
- Height from top of post down to top of crow standing on ground = $150$ cm
3. **Formula and Reasoning:**
The total height from ground to top of crow on post includes the height of the post plus the height of the crow.
If we let $h$ be the height of the crow standing on the ground, then:
$$\text{Height of post} + h = 210$$
From the second measurement, the height from the top of the post down to the top of the crow on the ground is $150$ cm, so:
$$\text{Height of post} - h = 150$$
4. **Set up the system of equations:**
$$\begin{cases}
\text{Height of post} + h = 210 \\
\text{Height of post} - h = 150
\end{cases}$$
5. **Add the two equations to eliminate $h$: **
$$ (\text{Height of post} + h) + (\text{Height of post} - h) = 210 + 150 $$
$$ 2 \times \text{Height of post} = 360 $$
$$ \text{Height of post} = \frac{360}{2} = 180 $$
6. **Substitute $\text{Height of post} = 180$ into the first equation:**
$$ 180 + h = 210 $$
$$ h = 210 - 180 = 30 $$
7. **Answer:** The height of the crow standing on the ground is $30$ cm.