Problem 55 - Algebra A Combined Function

Question

Scoville units are used to measure the hotness of a pepper. Measuring 577 thousand Scoville units, the "Red Savina" habañero pepper was known as the hottest chili pepper. That has recently changed with the discovery of Naga Jolokia pepper from India. It measures \(48 \%\) hotter than the habañero. Find the measure of the Naga Jolokia pepper. Round to the nearest thousand units.

Step-by-Step Solution

Answer

The Naga Jolokia measures 854,000 Scoville units.

Step 1: Identify given values

Start by identifying the values given in the problem. The original Scoville units of the "Red Savina" habañero pepper is 577,000. The Naga Jolokia pepper is 48% hotter than the habañero.

Step 2: Calculate the increase

To find the increase in Scoville units, calculate 48% of the habañero's Scoville units. Use the formula:\[\text{Increase} = \text{Original} \times \frac{\text{Percentage Increase}}{100}\]Substitute the values:\[\text{Increase} = 577,000 \times \frac{48}{100} = 277,000\]

Step 3: Calculate the Naga Jolokia's Scoville units

Add the increase to the original number of units to find the Naga Jolokia's Scoville measure:\[\text{Naga Jolokia units} = \text{Original units} + \text{Increase}\]\[\text{Naga Jolokia units} = 577,000 + 277,000\]

Step 4: Final calculation

Perform the addition:\[\text{Naga Jolokia units} = 854,000\]Round to the nearest thousand units to confirm: The number is already at the nearest thousand.

Key Concepts

Understanding Algebra Word Problems

Algebra word problems may seem daunting at first, but breaking them down into smaller steps can make them manageable. In this exercise, we are using algebra to determine the Scoville units for a new type of chili pepper. When faced with similar problems, follow these steps:

• Identify the known quantities: Here, it's the Scoville units of the Red Savina pepper and the percentage increase for the Naga Jolokia pepper.
• Apply algebraic expressions and operations: Use percentage increase calculations as part of your solution.
• Perform step-by-step calculations to find the unknown value: Determine the increase, then use it to find the desired measurement.

When solving these problems, ensure each step is clear and logical. This not only helps in arriving at the correct answer but also improves your mathematical reasoning skills.

Exploring Scoville Units

Scoville units are a measure of the pungency or spiciness of chili peppers and other spicy foods. They are named after their creator, Wilbur Scoville, who developed a method for measuring pepper heat levels.

• Scale: The Scoville scale is a measure based on the concentration of capsaicinoids, the chemical compounds responsible for the spicy sensation.
• Testing: Originally, the Scoville test involved a taste-test with human subjects to determine levels of dilution until the heat can no longer be detected, but more modern methods utilize High Performance Liquid Chromatography (HPLC).
• Unit Interpretation: Higher numbers on the Scoville scale mean a hotter pepper. For example, 577,000 Scoville units mean a relatively high level of heat.

Understanding Scoville units helps consumers and culinary professionals gauge the intensity and potential uses of different peppers.

Hottest Chili Pepper Measurement

Measuring the heat of chili peppers is an interesting and competitive area in both culinary and horticultural fields. The exercise involving the Naga Jolokia pepper shows how this competition can lead to the discovery of new species with unique properties.

• Historical context: For many years, the Red Savina habañero held the title of the hottest pepper before researchers in India discovered the Naga Jolokia—also known as the Ghost Pepper.
• Calculation of heat: Determining just how much hotter one pepper is than another involves percentage increase calculations, an important mathematical concept in these measurements.
• Practical implications: These measurements influence food production, spice blends, and even hot sauce competitions.

Recognizing how new measurements can impact existing records—and understanding the math involved—demonstrates the dynamic nature of this field.