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A grocery store sells apples by the pound. If the price per pound is i
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05 Apr 2021, 07:36
05 Apr 2021, 07:36
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A grocery store sells apples by the pound. If the price per pound is increased by $1, $12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store?
A. $4
B. $4.5
C. $5
D. $5.5
E. $6
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. $4
B. $4.5
C. $5
D. $5.5
E. $6
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: A grocery store sells apples by the pound. If the price per pound is i
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05 Apr 2021, 07:46
05 Apr 2021, 07:46
1
Carcass wrote:
A grocery store sells apples by the pound. If the price per pound is increased by $1, $12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store?
A. $4
B. $4.5
C. $5
D. $5.5
E. $6
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. $4
B. $4.5
C. $5
D. $5.5
E. $6
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
One approach here is to test the answer choices.
There is an algebraic approach:
let C = CURRENT price per pound
So, C + 1 = INCREASED price per pound
If the price per pound is increased by $1, $12 will buy 0.4 pounds less of apples than if the price remains at the current level.
Let's first turn this statement into a word equation
We can write: pounds of apples that can be purchased with $12 at CURRENT price - 0.4 = pounds of apples that can be purchased with $12 at INCREASED price
Convert to algebraic expression: 12/C - 0.4 = 12/(C + 1)
Rewrite as: 12/C - 0.4C/C = 12/(C + 1)
Combine terms: (12 - 0.4C)/C = 12/(C + 1)
Cross multiply: (12 - 0.4C)(C + 1) = (12)(C)
Expand and simplify: -0.4C² + 11.6C + 12 = 12C
Rearrange: 0.4C² + 0.4C - 12 = 0
Multiply both sides by 10 to get: 4C² + 4C - 120 = 0
Divide both sides by 4 to get: C² + C - 30 = 0
Factor: (C - 5)(C + 6) = 0
So, EITHER C = 5 OR C = -6
Since C cannot have a NEGATIVE value, we can be certain that C = 5
Answer: C
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A grocery store sells apples by the pound. If the price per pound is i
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06 Apr 2021, 03:59
06 Apr 2021, 03:59
1
Carcass wrote:
A grocery store sells apples by the pound. If the price per pound is increased by $1, $12 will buy 0.4 pounds less of apples than if the price remains at the current level. What is the current price per pound of apples at the grocery store?
A. $4
B. $4.5
C. $5
D. $5.5
E. $6
A. $4
B. $4.5
C. $5
D. $5.5
E. $6
Amount spent = \($12\) = (Cost per pound)(pounds of apples)
Let's check the option choices!
A. Cost per pound = \($4\), Pounds of apples = \(\frac{12}{4} = 3\)
Cost per pound = \($5\), Pounds of apples = \(\frac{12}{5} = 2.4\)
Difference = \(0.6\)
B. Cost per pound = \($4.5\), Pounds of apples = \(\frac{12}{4.5} = 2.667\)
Cost per pound = \($5.5\), Pounds of apples = \(\frac{12}{5.5} = 2.1818\)
Difference = \(0.486\)
C. Cost per pound = \($5\), Pounds of apples = \(\frac{12}{5} = 2.4\)
Cost per pound = \($2\), Pounds of apples = \(\frac{12}{6} = 2\)
Difference = \(0.4\)
Hence, option C
