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
I'm confused how to set up the formulas here. Can any experts help?
A grocery store sells apples by the pound. If the price per
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let C = CURRENT price per poundardz24 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
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: 0.4CÂ² + 12.4C  12 = 12C
Rearrange: 0.4CÂ² + 0.4C  12 = 0
Multiply both sides by 10 to get: 4CÂ² + 4C  120 = 0
Divide both sides by 4 to get: CÂ² + 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
Cheers,
Brent
Hi ardz24, you can try as follow,
Let's say the current cost of the apple be A.
No of pounds that can be bought with when the cost is A for $12 = 12/A.
Now, the new cost is A+1.
No of pounds that can be bought with when the cost is A+1 = 12/(A+1).
Per question stem, we have current pound when cost is A  pound when cost is A+1 = 0.4.
(12/A)  (12/(A+1)) = 0.4.
Solving gives a quadratic equation with A = 6.5 and A = 5. As the cost is positive, then A = 5. Option C.
Regards!
Let's say the current cost of the apple be A.
No of pounds that can be bought with when the cost is A for $12 = 12/A.
Now, the new cost is A+1.
No of pounds that can be bought with when the cost is A+1 = 12/(A+1).
Per question stem, we have current pound when cost is A  pound when cost is A+1 = 0.4.
(12/A)  (12/(A+1)) = 0.4.
Solving gives a quadratic equation with A = 6.5 and A = 5. As the cost is positive, then A = 5. Option C.
Regards!
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You could also backsolve. Typically, you want to test B, C, or D first, and then adjust accordingly. Because C is the only integer of the bunch, it would make sense to start there.ardz24 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
I'm confused how to set up the formulas here. Can any experts help?
If the price/pound = $5, then $12 would buy 12/5 = 2.4 pounds of apples.
If the price/pound increased by $1, it would be $6. Now $12 would buy 12/6 = 2 pounds of apples. Thus the weight of apples you could purchase would have decreased by 2.4  2 = .4 pounds. That's what we want! C is the answer.
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And as a public service announcement, if you are in a grocery store that's charging $5/pound for apples, you should leave this store at once.[email protected] wrote:You could also backsolve. Typically, you want to test B, C, or D first, and then adjust accordingly. Because C is the only integer of the bunch, it would make sense to start there.ardz24 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
I'm confused how to set up the formulas here. Can any experts help?
If the price/pound = $5, then $12 would buy 12/5 = 2.4 pounds of apples.
If the price/pound increased by $1, it would be $6. Now $12 would buy 12/6 = 2 pounds of apples. Thus the weight of apples you could purchase would have decreased by 2.4  2 = .4 pounds. That's what we want! C is the answer.
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We can PLUG IN THE ANSWERS, which represent the current price per pound.ardz24 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
When the current price per pound increases by $1, the number of pounds that can be purchased with $12 decreases by 0.4  implying that the number of pounds that can be purchased with $120 must decrease by 4.
The reasoning behind the statement in blue:
If the amount of money spent increases by a factor of 10 to $120, then the decrease in weight must also increase by a factor of 10 to 4 pounds.
Since the weight decrease for $120 is an INTEGER VALUE, the correct answer is almost certain to be a factor of $120.
Thus, the correct answer is likely to be A, C, or E.
Start with option in the middle: C.
When the correct answer is increased by $1, $120 must buy 4 fewer pounds.
C: $5 per pound
At a price $5 per pound, the number of pounds that can be purchased with $120 = 120/5 = 24.
After the price increases by $1 to $6 per pound, the number of pounds that can be purchased with $120 = 120/6 = 20.
Weight decrease = 2420 = 4.
Success!
The correct answer is C.
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We can let p = the current price per pound and a = the current number of pounds of apples that can be bought with $12 and create the equations:ardz24 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
pa = 12
a = 12/p
and
(p + 1)(a  0.4) = 12
pa + a  0.4p  0.4 = 12
Substituting, we have:
12 + 12/p  0.4p  0.4 = 12
12/p  0.4p  0.4 = 0
Multiplying by p, we have:
12  0.4p^2  0.4p = 0
0.4p^2 + 0.4p  12 = 0
Dividing by 0.4, we have:
p^2 + p  30 = 0
(p + 6)(p  5) = 0
p = 6 or p = 5
Since p can't be negative, p = 5.
Answer: C
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