You are to fix dinners for 400 people at a convention of Mexican food fans. Your recipe calls for 2 jalapeño peppers per serving (one serving per person). However, you have only habanero peppers on hand. The spiciness of peppers is measured in terms of the scoville heat unit (SHU). On average, one jalapeño pepper has a spiciness of 4000 SHU and one habanero pepper has a spiciness of 300000 SHU. To get the desired spiciness, how many habanero peppers should you substitute for the jalapeño peppers in the recipe for the 400 dinners?

The spiciness of one jalapeno pepper is 4000 SHU.

The spiciness of one habanero pepper is 300000 SHU.

The conversion factors can be used to convert the physical quantity from one unit to another unit. Using the given conversion factors, find the number of habanero peppers that should be substituted for the jalapeno peppers in the recipe for 400 dinners.

For one person 2jalapeno peppers are served.

The spiciness of 1 jalapeno pepper=4000 SHU.

The spiciness of 1 habanero pepper=300000 SHU.

Therefore, for 400 people, 800 jalapeno peppers should be served.

Therefore, total spiciness should be,

$(8000\times 4000)=3200000\mathrm{SHU}$

The number of habanero peppers that should be substituted for the jalapeno peppers in the recipe for 400 dinners is calculated as:

$$\begin{gathered} \frac{3200000}{300000}=10.67 \\ \approx 10.7 \end{gathered}$$

Thus, the number of habanero peppers that should be substituted for the jalapeno peppers is 10.7 .