How do you find the number of liters of 20% acid solution in a new mixture of 16% acid solution formed by mixing 12 liters of 8% acid solution with a 20% acid solution?

  

9.04 Semester Assessment: Algebra I Semester A, Part 2
Math | Graded Assignment | Semester Test, Part 2 | Algebra I
Name:
Date:
Graded Assignment
Semester Test, Part 2: Algebra I
Show all your work.
Total score: ____ of 45 points
(Score for Question 1: ___ of 14 points)
1. Roman mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. Find
the number of liters of 20% acid solution in the new mixture. Construct a table to organize the information,
and show all of your work to solve the problem.
Answer:
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Math | Graded Assignment | Semester Test, Part 2 | Algebra I
(Score for Question 2: ___ of 9 points)
2. The length of a rectangle is 5 mm longer than its width. Its perimeter is more than 30 mm. Let w equal the
width of the rectangle.
(a) Write an expression for the length in terms of the width.
(b) Use expressions for the length and width to write an inequality for the perimeter, on the basis of the
given information.
(c) Solve the inequality, clearly indicating the width of the rectangle.
Answer:
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Math | Graded Assignment | Semester Test, Part 2 | Algebra I
(Score for Question 3: ___ of 10 points)
3. Solve the system of equations using linear combination.
Answer:
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Math | Graded Assignment | Semester Test, Part 2 | Algebra I
(Score for Question 4: ___ of 12 points)
4. Gavin and Seiji both worked hard over the summer. Together, they earned a total of $425. Gavin earned $25
more than Seiji. How much did each of them earn?
(a) Write a system of two equations with two variables to model this problem.
(b) Use substitution or the elimination method to solve the system.
(c) Graph both equations.
(d) Answer the question.
Answer:
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Algebra I is a subject that deals with the use of variables and the rules of operations in solving mathematical equations. This subject is important for students as it forms the foundation for advanced mathematical concepts.

Description:

The Semester Assessment: Algebra I Semester A, Part 2 is a Graded Assignment that assesses the understanding of students on several mathematical concepts. The Math Semester Test, Part 2, is an Algebra I test that covers a diverse range of topics such as solving systems using linear combination, algebraic expressions, and inequality problem-solving. This test requires students to show their work and knowledge of algebraic formulas to solve complex mathematical equations. The test has four questions which must be answered correctly to achieve maximum points of 45. The questions range from finding liters of a solution, writing expressions based on given information, solving systems of equations, and modeling problems using algebraic equations. Students will benefit from this test as it will help them to gain a deeper understanding of algebra and its applications.

Objectives:
– To assess the student’s knowledge and skills in Algebra I Semester A, Part 2
– To evaluate the student’s ability to solve mathematical problems of varying complexity

Learning Outcomes:
By the end of this assessment, the student will be able to:
– Apply algebraic concepts to solve real-life problems involving mixtures, perimeters, and systems of equations
– Interpret and construct tables to organize information for problem-solving purposes
– Use substitution or elimination methods to solve systems of equations
– Graph two equations on the same coordinate plane and interpret their intersection in the context of the problem

Solution 1:

To solve question 1, Roman mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. We can find the number of liters of 20% acid solution in the new mixture by using the following table:

| Solution | Liters | % Acid |
|———-|——–|——–|
| 8% | 12 | 8 |
| 20% | x | 20 |
| Mixture | 12 + x | 16 |

We can set up the equation:

0.08(12) + 0.20x = 0.16(12 + x)

We can then solve for x and get the following:

0.96 + 0.20x = 1.92 + 0.16x

0.04x = 0.96

x = 24

Therefore, Solution 1 is: The number of liters of 20% acid solution in the new mixture is 24 liters.

Solution 2:

To solve question 4, Gavin and Seiji both worked hard over the summer and earned a total of $425. Gavin earned $25 more than Seiji. We can find how much each of them earned by using the following system of two equations with two variables:

Let x be Seiji’s earnings
Then Gavin’s earnings would be x + $25

x + (x + $25) = $425 (because their total earnings is $425)
2x + $25 = $425
2x = $400
x = $200

Therefore, Solution 2 is: Seiji earned $200 and Gavin earned $225.

Suggested Resources/Books:

1. Algebra I for Dummies by Mary Jane Sterling
2. Algebra I Workbook For Dummies by Mary Jane Sterling
3. Algebra I Essentials For Dummies by Mary Jane Sterling
4. Algebra I: Learn and Practice – Math Workbook with 1000+ questions and answers by Exam SAM

Similar Asked Questions:

1. How do you solve equations with linear combination method?
2. How do you solve inequalities with variables on both sides?
3. How do you graph linear equations on coordinate planes?
4. How do you find the slope and intercept of a line?
5. How do you solve word problems related to algebraic equations?

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