11) Solve the problem. Write out your check and write your answer in complete sentence form including correct units. It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 70 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength? Show your work here: Write your sentence answer here using correct units: Write out your check here using the information from the original wording of the problem. Do not check by using your equation because that could be incorrect:
11) Solve the problem. Write out your check and write your answer in complete sentence form including correct units. It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 70 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength? Show your work here: Write your sentence answer here using correct units: Write out your check here using the information from the original wording of the problem. Do not check by using your equation because that could be incorrect:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
problem attached- need it written out and easy to follow.
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![### Problem-Solving: Antifreeze Solution Concentration
**Problem Statement:**
It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 70 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?
**Instructions:**
Solve the problem. Write out your check and write your answer in complete sentence form including correct units.
**Steps:**
1. **Form the Equation:**
Let \( x \) be the amount of 20% solution to be drained and replaced with 100% antifreeze.
Initial amount of antifreeze:
\[
0.20 \times 70 \text{ liters}
\]
Amount of antifreeze left after draining \( x \) liters of 20% solution:
\[
0.20(70 - x) \text{ liters}
\]
Amount of antifreeze added:
\[
x \text{ liters}
\]
Total antifreeze in the solution after replacement:
\[
0.20(70 - x) + x \text{ liters}
\]
This needs to equal 40% of the total solution (70 liters):
\[
0.40 \times 70 \text{ liters}
\]
2. **Solving the Equation:**
\[
0.20(70 - x) + x = 0.40 \times 70
\]
Simplify and solve for \( x \):
\[
14 - 0.20x + x = 28
\]
\[
14 + 0.80x = 28
\]
\[
0.80x = 14
\]
\[
x = \frac{14}{0.80}
\]
\[
x = 17.5 \text{ liters}
\]
**Answer:**
\[
\boxed{17.5 \text{ liters}}
\]
**Write your sentence answer here using correct units:**
To obtain a 40% antifreeze solution, 17.5 liters of the 20% solution should be drained and replaced with 17.5 liters of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29666072-4841-4557-93a0-541aeee2aafd%2F0f134ce1-aa94-4f41-9087-5d2d2b9dfaa2%2F7agykju_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem-Solving: Antifreeze Solution Concentration
**Problem Statement:**
It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 70 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?
**Instructions:**
Solve the problem. Write out your check and write your answer in complete sentence form including correct units.
**Steps:**
1. **Form the Equation:**
Let \( x \) be the amount of 20% solution to be drained and replaced with 100% antifreeze.
Initial amount of antifreeze:
\[
0.20 \times 70 \text{ liters}
\]
Amount of antifreeze left after draining \( x \) liters of 20% solution:
\[
0.20(70 - x) \text{ liters}
\]
Amount of antifreeze added:
\[
x \text{ liters}
\]
Total antifreeze in the solution after replacement:
\[
0.20(70 - x) + x \text{ liters}
\]
This needs to equal 40% of the total solution (70 liters):
\[
0.40 \times 70 \text{ liters}
\]
2. **Solving the Equation:**
\[
0.20(70 - x) + x = 0.40 \times 70
\]
Simplify and solve for \( x \):
\[
14 - 0.20x + x = 28
\]
\[
14 + 0.80x = 28
\]
\[
0.80x = 14
\]
\[
x = \frac{14}{0.80}
\]
\[
x = 17.5 \text{ liters}
\]
**Answer:**
\[
\boxed{17.5 \text{ liters}}
\]
**Write your sentence answer here using correct units:**
To obtain a 40% antifreeze solution, 17.5 liters of the 20% solution should be drained and replaced with 17.5 liters of
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