In a triple batch of a spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. How much salt is used with 8 teaspoons of garlic powder? If there are 14 teaspoons of spice mix, how much salt is in it?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Spice Mix Ratio Problem**

**Problem Statement:**
In a triple batch of a spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt.

First Question:
How much salt is used with 8 teaspoons of garlic powder?

Second Question:
If there are 14 teaspoons of spice mix, how much salt is in it?

**Explanation:**

1. To solve the first question, we need to determine the ratio between the garlic powder and the salt in the triple batch.

   - Triple batch contains:
     - Garlic powder: 6 teaspoons
     - Salt: 15 teaspoons
     
     Let's simplify the ratio: 
     \[
     \text{Ratio} = \frac{6 \text{ tsp garlic powder}}{15 \text{ tsp salt}} = \frac{2}{5}
     \]

   - We need to find out how much salt corresponds to 8 teaspoons of garlic powder:
     \[
     \frac{2 \text{ tsp garlic powder}}{5 \text{ tsp salt}} = \frac{8 \text{ tsp garlic powder}}{x \text{ tsp salt}}
     \]
     Solving for \( x \):
     \[
     x = \frac{8 \text{ tsp garlic powder} \times 5 \text{ tsp salt}}{2 \text{ tsp garlic powder}} = 20 \text{ tsp salt}
     \]

2. To answer the second question, we first need to determine the total amount in a single batch to see the consistent ratio throughout multiple batches.
    
    - Total spice mix in a triple batch:
      \[
      \text{Total} = 6 \text{ tsp garlic powder} + 15 \text{ tsp salt} = 21 \text{ tsp spice mix} 
      \]
    - From this, we need to find the salt portion in 14 teaspoons of the spice mix:
      \[
      \frac{15 \text{ tsp salt}}{21 \text{ tsp spice mix}} = \frac{x \text{ tsp salt}}{14 \text{ tsp spice mix}}
      \]
      Solving for \( x \):
      \[
      x = \frac{15 \text{ tsp salt} \times 14 \text{ tsp spice mix}}{21 \text{ tsp spice mix}} = 10 \text{ tsp salt}
      \]

These calculations
Transcribed Image Text:**Spice Mix Ratio Problem** **Problem Statement:** In a triple batch of a spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. First Question: How much salt is used with 8 teaspoons of garlic powder? Second Question: If there are 14 teaspoons of spice mix, how much salt is in it? **Explanation:** 1. To solve the first question, we need to determine the ratio between the garlic powder and the salt in the triple batch. - Triple batch contains: - Garlic powder: 6 teaspoons - Salt: 15 teaspoons Let's simplify the ratio: \[ \text{Ratio} = \frac{6 \text{ tsp garlic powder}}{15 \text{ tsp salt}} = \frac{2}{5} \] - We need to find out how much salt corresponds to 8 teaspoons of garlic powder: \[ \frac{2 \text{ tsp garlic powder}}{5 \text{ tsp salt}} = \frac{8 \text{ tsp garlic powder}}{x \text{ tsp salt}} \] Solving for \( x \): \[ x = \frac{8 \text{ tsp garlic powder} \times 5 \text{ tsp salt}}{2 \text{ tsp garlic powder}} = 20 \text{ tsp salt} \] 2. To answer the second question, we first need to determine the total amount in a single batch to see the consistent ratio throughout multiple batches. - Total spice mix in a triple batch: \[ \text{Total} = 6 \text{ tsp garlic powder} + 15 \text{ tsp salt} = 21 \text{ tsp spice mix} \] - From this, we need to find the salt portion in 14 teaspoons of the spice mix: \[ \frac{15 \text{ tsp salt}}{21 \text{ tsp spice mix}} = \frac{x \text{ tsp salt}}{14 \text{ tsp spice mix}} \] Solving for \( x \): \[ x = \frac{15 \text{ tsp salt} \times 14 \text{ tsp spice mix}}{21 \text{ tsp spice mix}} = 10 \text{ tsp salt} \] These calculations
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