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The corner store sells yams and plantains by the pound. A
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27 May 2018, 12:24
27 May 2018, 12:24
Expert Reply
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Question Stats:
72% (01:30) correct
27% (02:11) wrong based on 101 sessions
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The corner store sells yams and plantains by the pound. A pound of plantains cost $0.30 less than twice the cost of a pound of yams.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The cost of two pounds of yams and two pounds of plantains |
The cost of three pounds of plantains |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: The corner store sells yams and plantains by the pound. A
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27 May 2018, 13:18
27 May 2018, 13:18
2
Expert Reply
Explanation
Represent the cost per pound of the vegetables by their first letters.
The given information translates to p = 2y – 0.30 because “twice” means multiply by two and “less” indicates subtraction. Then, translate the quantities into algebraic expressions:
Quantity A = 2y + 2p
Quantity B = 3p
Since 2p is common to both quantities, it can be subtracted without changing their relative values:
Quantity A = 2y
Quantity B = p
Since p = 2y – 0.30, Quantity B is 0.30 less than Quantity A.
Hence option A is correct!
Represent the cost per pound of the vegetables by their first letters.
The given information translates to p = 2y – 0.30 because “twice” means multiply by two and “less” indicates subtraction. Then, translate the quantities into algebraic expressions:
Quantity A = 2y + 2p
Quantity B = 3p
Since 2p is common to both quantities, it can be subtracted without changing their relative values:
Quantity A = 2y
Quantity B = p
Since p = 2y – 0.30, Quantity B is 0.30 less than Quantity A.
Hence option A is correct!
Re: The corner store sells yams and plantains by the pound. A
[#permalink]
20 Jun 2023, 10:18
20 Jun 2023, 10:18
Translate the stem:
Let p=price of plantains, y=price of yam
p=2y-30
QA:
2 lbs of Plantains and 2 lbs of Yam can be expressed as:
2p+2y
Substituting the stem equation:
2(2y-30)+2y
6y-60
QB:
3 lbs of plantains will cost 3p
3(2y-30)=6y-90
As y will be some non-negative quantity (prices cannot be negative), 6y-60 is always larger than 6y-90.
QA>QB, always
A
Let p=price of plantains, y=price of yam
p=2y-30
QA:
2 lbs of Plantains and 2 lbs of Yam can be expressed as:
2p+2y
Substituting the stem equation:
2(2y-30)+2y
6y-60
QB:
3 lbs of plantains will cost 3p
3(2y-30)=6y-90
As y will be some non-negative quantity (prices cannot be negative), 6y-60 is always larger than 6y-90.
QA>QB, always
A
