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20 Aug 2025, 10:47
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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:
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Question Stats:
100% (02:50) correct
0% (00:00) wrong based on 1 sessions
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The cost of ten hot dogs and nine pretzels is $74.15. The cost of nine hot dogs and ten pretzels is $74.05.
Quantity A
The cost of one hot dog
Quantity B
The cost of one pretzel
Quantity A
The cost of one hot dog
Quantity B
The cost of one pretzel
30 Aug 2025, 04:48
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Official Explanation
In the second sentence given, there is one fewer hot dog but one more pretzel. Replacing one hot dog with one pretzel decreases the total cost, so the pretzel must be cheaper. Then the cost of the hot dog, Quantity (A), is greater.
Represent the information with a linear system. If x is the price of one hot dog and y is the price of one pretzel, then \(10x + 9y = 74.15,\) and \(9x + 10y = 74.05.\) Try lining up the equations vertically and subtracting to find some type of cancellation. Adding y to each side reveals that \(x = y + .10,\) so the cost of the hot dog is $.10 more than the cost of the pretzel, and (A) is greater.
The on-screen calculator makes the traditional elimination method possible, but since this approach is much longer, try to spot one of the easier ways first. Set up a linear system, as in (*) above. Then multiply the first equation by 9 and the second equation by -10, so that the x coefficients become equal but opposite in sign. Some number crunching shows that Add the two whole equations together to obtain \(-19y = -73.15.\) Dividing both sides by -19 shows that y = $3.85. Finally, substitute this value back into one of the original equations and solve for x, to obtain x = $3.95, and (A) is greater.
Answer: A
In the second sentence given, there is one fewer hot dog but one more pretzel. Replacing one hot dog with one pretzel decreases the total cost, so the pretzel must be cheaper. Then the cost of the hot dog, Quantity (A), is greater.
Represent the information with a linear system. If x is the price of one hot dog and y is the price of one pretzel, then \(10x + 9y = 74.15,\) and \(9x + 10y = 74.05.\) Try lining up the equations vertically and subtracting to find some type of cancellation. Adding y to each side reveals that \(x = y + .10,\) so the cost of the hot dog is $.10 more than the cost of the pretzel, and (A) is greater.
The on-screen calculator makes the traditional elimination method possible, but since this approach is much longer, try to spot one of the easier ways first. Set up a linear system, as in (*) above. Then multiply the first equation by 9 and the second equation by -10, so that the x coefficients become equal but opposite in sign. Some number crunching shows that Add the two whole equations together to obtain \(-19y = -73.15.\) Dividing both sides by -19 shows that y = $3.85. Finally, substitute this value back into one of the original equations and solve for x, to obtain x = $3.95, and (A) is greater.
Answer: A
