7 ### Problem StatementA druggist has two mixtures of a certain chemical and water, one containing 10% of the chemical and the other containing 40% of the chemical. How much of each mixture should he use to make 10 ounces that contain 25% of the chemical?If $ x $ is the amount of 10% mixture used, then which expression represents the ounces of chemical contained in it?- \[ ] x- \[ ] 10x- \[ ] 0.1x### ExplanationTo solve this problem, we need to set up equations based on the information given and understand the relationship between the different mixtures.1. **Define Variables:** - Let $ x $ be the amount of the 10% mixture used. - Consequently, the amount of the 40% mixture used will be $ 10 - x $ ounces because the total mixture amounts to 10 ounces.2. **Form Equations Based on Concentrations:** - The amount of chemical in the 10% mixture is $ 0.10x $ ounces. - The amount of chemical in the 40% mixture is $ 0.40(10 - x) $ ounces.3. **Total Concentration Requirement:** - The total mixture should contain 25% of the chemical, so the total chemical content should be $ 0.25 \times 10 $ = 2.5 ounces.4. **Set Up the Equation:** \[ 0.10x + 0.4(10 - x) = 2.5 \]5. **Simplify the Equation:** \[ 0.10x + 4 - 0.4x = 2.5 \] \[ 4 - 0.3x = 2.5 \] \[ -0.3x = 2.5 - 4 \] \[ -0.3x = -1.5 \] \[ x = \frac{-1.5}{-0.3} = 5 \]6. **Calculate Amounts:** - $ x = 5 $ ounces of the 10% mixture. - $ 10 - x = 5 $

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A druggist has two mixtures of a certain chemical and water, one containing 10% of the chemical and the other containing 40% of the chemical. How much of each mixture should he use to make 10 ounces that contain 25% of the chemical? If x is the amount of 10% mixture used, then which expression represents the ounces of chemical contained in it? O 10x 0.1x

A druggist has two mixtures of a certain chemical and water, one containing 10% of the chemical and the other containing 40% of the chemical. How much of each mixture should he use to make 10 ounces that contain 25% of the chemical? If x is the amount of 10% mixture used, then which expression represents the ounces of chemical contained in it? O 10x 0.1x

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

### Problem Statement

A druggist has two mixtures of a certain chemical and water, one containing 10% of the chemical and the other containing 40% of the chemical. How much of each mixture should he use to make 10 ounces that contain 25% of the chemical?

If $ x $ is the amount of 10% mixture used, then which expression represents the ounces of chemical contained in it?

- \[ ] x
- \[ ] 10x
- \[ ] 0.1x

### Explanation

To solve this problem, we need to set up equations based on the information given and understand the relationship between the different mixtures.

1. **Define Variables:**
- Let $ x $ be the amount of the 10% mixture used.
- Consequently, the amount of the 40% mixture used will be $ 10 - x $ ounces because the total mixture amounts to 10 ounces.

2. **Form Equations Based on Concentrations:**
- The amount of chemical in the 10% mixture is $ 0.10x $ ounces.
- The amount of chemical in the 40% mixture is $ 0.40(10 - x) $ ounces.

3. **Total Concentration Requirement:**
- The total mixture should contain 25% of the chemical, so the total chemical content should be $ 0.25 \times 10 $ = 2.5 ounces.

4. **Set Up the Equation:**
\[
0.10x + 0.4(10 - x) = 2.5
\]

5. **Simplify the Equation:**
\[
0.10x + 4 - 0.4x = 2.5
\]
\[
4 - 0.3x = 2.5
\]
\[
-0.3x = 2.5 - 4
\]
\[
-0.3x = -1.5
\]
\[
x = \frac{-1.5}{-0.3} = 5
\]

6. **Calculate Amounts:**
- $ x = 5 $ ounces of the 10% mixture.
- $ 10 - x = 5 $

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