The height of a plant increases by `16%` in one week. If the increases height is 29 cm, find the original height.

Answer

To find the original height of the plant before the increase, we can follow these steps:

### Step 1: Define the original height
Let the original height of the plant be \( x \) cm.

### Step 2: Write the equation for the increase
According to the problem, the height of the plant increases by \( 16\% \) in one week, and the increase in height is given as \( 29 \) cm. We can express this mathematically as:
\[ x + 16\% \text{ of } x = 29 \text{ cm} \]
This can be rewritten as:
\[ x + \frac{16}{100} \times x = 29 \]

### Step 3: Combine like terms
To combine the terms on the left side, we can factor out \( x \):
\[ x + \frac{16}{100}x = 29 \]
This simplifies to:
\[ x \left(1 + \frac{16}{100}\right) = 29 \]
Calculating \( 1 + \frac{16}{100} \):
\[ 1 + \frac{16}{100} = \frac{100}{100} + \frac{16}{100} = \frac{116}{100} \]
So, we have:
\[ \frac{116}{100}x = 29 \]

### Step 4: Solve for \( x \)
To isolate \( x \), we multiply both sides by \( \frac{100}{116} \):
\[ x = 29 \times \frac{100}{116} \]

### Step 5: Calculate the value
Now, we can calculate the value:
\[ x = \frac{2900}{116} \]
Dividing \( 2900 \) by \( 116 \):
\[ x = 25 \]

### Conclusion
The original height of the plant is \( 25 \) cm.

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