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Chapter 1: Problem 57

You are to fix dinners for 400 people at a convention of Mexican food fans. Your recipe calls for 2 jalape帽o 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 jalape帽o pepper has a spiciness of \(4000 \mathrm{SHU}\) and one habanero pepper has a spiciness of 300000 SHU. To get the desired spiciness, how many habanero peppers should you substitute for the jalape帽o peppers in the recipe for the 400 dinners?

Short Answer

Expert verified
Substitute 11 habanero peppers for the jalape帽o peppers.

Step by step solution

01

Determine Total Jalape帽o Peppers Needed

The recipe requires 2 jalape帽o peppers per serving. Since there are 400 people, we calculate the total number of jalape帽o peppers needed as follows: \[ 2 \text{ peppers/person} \times 400 \text{ people} = 800 \text{ jalape帽o peppers} \]
02

Calculate Total Spiciness of Jalape帽o Peppers

Each jalape帽o pepper has 4000 SHU. Calculate the total spiciness for all 800 jalape帽o peppers:\[ 800 \text{ peppers} \times 4000 \text{ SHU/pepper} = 3200000 \text{ SHU} \]
03

Calculate Number of Habanero Peppers Needed

Each habanero pepper has 300000 SHU. To achieve the total spiciness needed (3200000 SHU), calculate the number of habanero peppers required:\[ \frac{3200000 \text{ SHU}}{300000 \text{ SHU/pepper}} = \frac{32}{3} \approx 10.67 \]
04

Round Up the Number of Habanero Peppers

Since you can't use a fraction of a pepper, round up the result from Step 3 to the nearest whole number:\[ \approx 11 \text{ habanero peppers} \]Rounding up ensures that the total spiciness meets or exceeds the required 3200000 SHU.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Scoville Heat Unit
The Scoville Heat Unit (SHU) is a measure that tells us how spicy a pepper is. Created by Wilbur Scoville in 1912, it's a way to rank the heat of various peppers. The number represents the amount of capsaicin, the chemical compound responsible for the spicy sensation. The higher the SHU, the spicier the pepper.

Knowing the SHU is helpful when cooking, especially if you're aiming for a specific level of heat in your dish. For example, a jalape帽o might have around 4,000 SHU, while a habanero can have a scorching 300,000 SHU. This big difference is what makes pepper substitution a bit tricky.
  • Low SHU: Peppers like bell peppers have little to no spiciness.
  • Medium SHU: Peppers like jalape帽os provide a moderate kick.
  • High SHU: Peppers like habaneros deliver intense heat.
Understanding SHU allows cooks to make better decisions regarding ingredient substitutions, ensuring the final dish has the desired level of spiciness.
Pepper Substitution
Sometimes, you might have to use different peppers than originally called for in a recipe. This is known as pepper substitution. It's important to understand the Scoville Heat Unit rating of each type of pepper you're considering. When substituting, you aim to keep the spiciness level the same by adjusting the quantity of the peppers used.

In the example exercise, we needed to find out how many habanero peppers would match the spiciness of the jalape帽o peppers. Using math, we calculated that for 400 meals, a total heat of 3,200,000 SHU was necessary, previously achieved by 800 jalape帽o peppers. Since habaneros provide more SHU per pepper, fewer of them are necessary.
  • Calculate the total SHU needed based on original peppers.
  • Determine SHU of the substitute pepper (habanero in this case).
  • Use the formula \( \text{Total Jalape帽o SHU} / \text{Habanero SHU per pepper} \) to find out how many habaneros are required.
This approach ensures the dish has the same level of spiciness as the original recipe intended.
Jalape帽o and Habanero Peppers
Jalape帽o and habanero peppers are two popular types of chili peppers with distinctive differences in flavor and heat. Jalape帽os are common in many cuisines and are known for their mild, versatile heat. With a Scoville Heat Unit range between 2,500 to 8,000, they add a subtle kick without overwhelming the dish.

Habanero peppers, on the other hand, are for those who can handle fiery heat. With SHU values ranging from 100,000 to 350,000, these peppers pack quite a punch and are used sparingly in recipes. They are often included in hot sauces and spicy dishes where intense heat is desired.
  • Jalape帽o Uses: Slices on nachos, fresh in salsas, or stuffed for appetizers.
  • Habanero Uses: Blending in hot sauces, adding a kick to stews, and spicing up seafood dishes.
Understanding both the flavor and heat level of jalape帽o and habanero peppers allows for better use in recipes and more successful substitutions when necessary.

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Most popular questions from this chapter

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As a contrast between the old and the modern and between the large and the small, consider the following: In old rural England 1 hide (between 100 and 120 acres) was the area of land needed to sustain one family with a single plough for one year. (An area of 1 acre is equal to \(4047 \mathrm{~m}^{2} .\) ) Also, 1 wapentake was the area of land needed by 100 such families. In quantum physics, the cross-sectional area of a nucleus (defined in terms of the chance of a particle hitting and being absorbed by it ) is measured in units of barns, where 1 barn is \(1 \times 10^{-28} \mathrm{~m}^{2}\). (In nuclear physics jargon, if a nucleus is "large," then shooting a particle at it is like shooting a bullet at a barn door, which can hardly be missed.) What is the ratio of 25 wapentakes to 11 barns?
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