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09 Sep 2024, 13:11
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
66% (03:59) correct
33% (02:40) wrong based on 3 sessions
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At the beginning of a trip, the tank of Diana’s car was filled with gasoline to half of its capacity. During the trip, Diana used 30 percent of the gasoline in the tank. At the end of the trip, Diana added 8 gallons of gasoline to the tank. The capacity of the tank of Diana’s car was x gallons. Which of the following expressions represent the number of gallons of gasoline in the tank after Diana added gasoline to the tank at the end of the trip?
Indicate all such expressions.
A. \(\frac{x}{2}-\frac{3x}{20} + 8\)
B. \(\frac{7x}{20}+ 8\)
C. \(\frac{3x}{20}+ 8\)
D. \(\frac{x}{2}+\frac{3x}{20} - 8\)
E. \(\frac{7x}{20}- 8\)
Indicate all such expressions.
A. \(\frac{x}{2}-\frac{3x}{20} + 8\)
B. \(\frac{7x}{20}+ 8\)
C. \(\frac{3x}{20}+ 8\)
D. \(\frac{x}{2}+\frac{3x}{20} - 8\)
E. \(\frac{7x}{20}- 8\)
08 Feb 2025, 11:33
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OE
The capacity of the car’s tank was x gallons of gasoline. Before the trip, the tank was half full and therefore contained x/2 gallons of gasoline. During the trip, 30 percent of the gasoline in the tank was used, so the number of gallons lef was 70 percent of x/2, or \((\frac{7}{10})(\frac{x}{2})= \frac{7x}{20}\). After Diana added 8 gallons of gasoline to the tank, the total number of gallons in the tank was \(\frac{7x}{20} + 8\). Thus one correct choice is Choice B, \(\frac{7x}{20}+8.\) However, the question asks you to fnd all of the answer choices that represent the number of gallons of gasoline in the tank at the end of the trip. So you need to determine whether any of the other choices are equivalent to \(\frac{7x}{20} + 8\). Of the answer choices, only Choices A and C have the same constant term as Choice B: 8. So these are the only choices that need to be checked. Choice A, \(\frac{x}{2}-\frac{3x}{20}+ 8\), can be simplifed as follows.
\(\frac{x}{2}-\frac{3x}{20}+ 8 =\frac{10x}{20}-\frac{3x}{20}+ 8 =\frac{7x}{20}\)
So Choice A is equivalent to \(\frac{7x}{20}+ 8\). Choice C, \(\frac{3x}{20}+ 8\), is clearly not equivalent to \(\frac{7x}{20} + 8\). Thus the correct answer consists of Choices A and B.
The capacity of the car’s tank was x gallons of gasoline. Before the trip, the tank was half full and therefore contained x/2 gallons of gasoline. During the trip, 30 percent of the gasoline in the tank was used, so the number of gallons lef was 70 percent of x/2, or \((\frac{7}{10})(\frac{x}{2})= \frac{7x}{20}\). After Diana added 8 gallons of gasoline to the tank, the total number of gallons in the tank was \(\frac{7x}{20} + 8\). Thus one correct choice is Choice B, \(\frac{7x}{20}+8.\) However, the question asks you to fnd all of the answer choices that represent the number of gallons of gasoline in the tank at the end of the trip. So you need to determine whether any of the other choices are equivalent to \(\frac{7x}{20} + 8\). Of the answer choices, only Choices A and C have the same constant term as Choice B: 8. So these are the only choices that need to be checked. Choice A, \(\frac{x}{2}-\frac{3x}{20}+ 8\), can be simplifed as follows.
\(\frac{x}{2}-\frac{3x}{20}+ 8 =\frac{10x}{20}-\frac{3x}{20}+ 8 =\frac{7x}{20}\)
So Choice A is equivalent to \(\frac{7x}{20}+ 8\). Choice C, \(\frac{3x}{20}+ 8\), is clearly not equivalent to \(\frac{7x}{20} + 8\). Thus the correct answer consists of Choices A and B.
