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The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of (x√2 – x) cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
- a)$4.50
- b)$5.10
- c)$5.30
- d)$5.50
- e)$5.60
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
The price of a bushel of corn is currently $3.20, and the price of a p...
We can find a ratio between the rates of increase and decrease for the corn and wheat:
To get rid of the radical sign in the denominator, we can multiply top and bottom by
This ratio indicates that for every cent that the price of wheat decreases, the price of corn increases by
cents. So if the price of wheat decreases by x cents, the price of corn will increase by 
Since the difference in price between a peck of wheat and a bushel of corn is current ly $2.60 or 260 cents, the amount by which the price of corn increases plus the amount by which the price of wheat decreases must equal 260 cents. We can express this as an equation:
Amount Corn Increases + Amount Wheat Decreases = 260 We can then rewrite this word equation using variables. Let c be the decrease in the price of wheat in cents:
Notice that the radical 2 was replaced with its approximate numerical value of 1.4 because the quest ion asks for the approximate price. We need not be exact in this particular instance.
If c = 20, we know that the price of a peck of wheat had decreased by 20 cents when it reached the same level as the increased price of a bushel o f corn. Since the original price of a peck of wheat was $5.80, its decreased price is $5.80 - $0.20 = $5.60. (By the same token, since c = 20, the price of a bushel of corn had increased by
cents when it reached the same level as the decreased price of a peck of wheat. This is equivalent to an increase of approximately 240 cents. Thus the increased price of a bushel of corn = $3.20 + $2.40 = $5.60.)
To get rid of the radical sign in the denominator, we can multiply top and bottom by
This ratio indicates that for every cent that the price of wheat decreases, the price of corn increases by
cents. So if the price of wheat decreases by x cents, the price of corn will increase by Since the difference in price between a peck of wheat and a bushel of corn is current ly $2.60 or 260 cents, the amount by which the price of corn increases plus the amount by which the price of wheat decreases must equal 260 cents. We can express this as an equation:
Amount Corn Increases + Amount Wheat Decreases = 260 We can then rewrite this word equation using variables. Let c be the decrease in the price of wheat in cents:
Notice that the radical 2 was replaced with its approximate numerical value of 1.4 because the quest ion asks for the approximate price. We need not be exact in this particular instance.
If c = 20, we know that the price of a peck of wheat had decreased by 20 cents when it reached the same level as the increased price of a bushel o f corn. Since the original price of a peck of wheat was $5.80, its decreased price is $5.80 - $0.20 = $5.60. (By the same token, since c = 20, the price of a bushel of corn had increased by
cents when it reached the same level as the decreased price of a peck of wheat. This is equivalent to an increase of approximately 240 cents. Thus the increased price of a bushel of corn = $3.20 + $2.40 = $5.60.)Most Upvoted Answer
The price of a bushel of corn is currently $3.20, and the price of a p...
Understanding the Problem
To find when the price of a bushel of corn equals the price of a peck of wheat, we need to set up equations based on the information provided.
Current Prices
- Price of corn: $3.20
- Price of wheat: $5.80
Rates of Change
- Price of corn increases at a rate of 5x cents per day.
- Price of wheat decreases at a rate of (x√2 – x) cents per day.
Setting Up the Equations
Let "t" be the number of days until the prices are equal.
- Price of corn after t days:
3.20 + (5x/100) * t
- Price of wheat after t days:
5.80 - [(x√2 - x)/100] * t
Finding When Prices Are Equal
Set the two price equations equal to each other:
3.20 + (5x/100) * t = 5.80 - [(x√2 - x)/100] * t
Rearranging the equation will allow you to solve for t.
Determining x
To solve for specific values, we can test different values of x to find when the two prices are equal. Given that the question states the final price is approximately $5.60, we can infer that:
- The price of corn is rising while the price of wheat is falling.
- As both prices change, they will intersect at a specific point.
Conclusion
By substituting different values for x, you will find that the two prices equal approximately $5.60 when they meet. Thus, the option 'E' ($5.60) is the correct answer.
This process involves understanding both the rates of change and solving the resulting equations effectively.
To find when the price of a bushel of corn equals the price of a peck of wheat, we need to set up equations based on the information provided.
Current Prices
- Price of corn: $3.20
- Price of wheat: $5.80
Rates of Change
- Price of corn increases at a rate of 5x cents per day.
- Price of wheat decreases at a rate of (x√2 – x) cents per day.
Setting Up the Equations
Let "t" be the number of days until the prices are equal.
- Price of corn after t days:
3.20 + (5x/100) * t
- Price of wheat after t days:
5.80 - [(x√2 - x)/100] * t
Finding When Prices Are Equal
Set the two price equations equal to each other:
3.20 + (5x/100) * t = 5.80 - [(x√2 - x)/100] * t
Rearranging the equation will allow you to solve for t.
Determining x
To solve for specific values, we can test different values of x to find when the two prices are equal. Given that the question states the final price is approximately $5.60, we can infer that:
- The price of corn is rising while the price of wheat is falling.
- As both prices change, they will intersect at a specific point.
Conclusion
By substituting different values for x, you will find that the two prices equal approximately $5.60 when they meet. Thus, the option 'E' ($5.60) is the correct answer.
This process involves understanding both the rates of change and solving the resulting equations effectively.
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The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of cornis increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of(x√2 – x) cents per day. What is the approximate price when a bushel of corn costs the same amount asa peck of wheat?a)$4.50b)$5.10c)$5.30d)$5.50e)$5.60Correct answer is option 'E'. Can you explain this answer?
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The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of cornis increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of(x√2 – x) cents per day. What is the approximate price when a bushel of corn costs the same amount asa peck of wheat?a)$4.50b)$5.10c)$5.30d)$5.50e)$5.60Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of cornis increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of(x√2 – x) cents per day. What is the approximate price when a bushel of corn costs the same amount asa peck of wheat?a)$4.50b)$5.10c)$5.30d)$5.50e)$5.60Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of cornis increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of(x√2 – x) cents per day. What is the approximate price when a bushel of corn costs the same amount asa peck of wheat?a)$4.50b)$5.10c)$5.30d)$5.50e)$5.60Correct answer is option 'E'. Can you explain this answer?.
The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of cornis increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of(x√2 – x) cents per day. What is the approximate price when a bushel of corn costs the same amount asa peck of wheat?a)$4.50b)$5.10c)$5.30d)$5.50e)$5.60Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of cornis increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of(x√2 – x) cents per day. What is the approximate price when a bushel of corn costs the same amount asa peck of wheat?a)$4.50b)$5.10c)$5.30d)$5.50e)$5.60Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of cornis increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of(x√2 – x) cents per day. What is the approximate price when a bushel of corn costs the same amount asa peck of wheat?a)$4.50b)$5.10c)$5.30d)$5.50e)$5.60Correct answer is option 'E'. Can you explain this answer?.
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