To find out how many seed packets the farmer needs to raise 16 plants, we start by determining the unit rate of plants per seed packet based on the initial information provided.
The farmer has grown 10 plants using 5 seed packets. Thus, we can calculate the number of plants per seed packet:
\[ \text{Plants per seed packet} = \frac{10 \text{ plants}}{5 \text{ seed packets}} = 2 \text{ plants per seed packet} \]
Now we need to find out how many seed packets are required to grow 16 plants. We can set up the following equation:
Let \( x \) be the number of seed packets needed for 16 plants. Using the unit rate we just calculated:
\[ \frac{16 \text{ plants}}{x \text{ seed packets}} = 2 \text{ plants per seed packet} \]
To find \( x \), we can rearrange this equation:
\[ x = \frac{16 \text{ plants}}{2 \text{ plants per seed packet}} = 8 \text{ seed packets} \]
So, the farmer needs 8 seed packets to raise 16 plants in his backyard.