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A grocery store sells apples by the pound. If the price per

This topic has 5 expert replies and 1 member reply

A grocery store sells apples by the pound. If the price per

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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

I'm confused how to set up the formulas here. Can any experts help?

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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
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 + 12.4C - 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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Brent

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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!

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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?
You could also back-solve. 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.

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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DavidG@VeritasPrep wrote:
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?
You could also back-solve. 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.

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.
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. Smile

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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
We can PLUG IN THE ANSWERS, which represent the current price per pound.

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 = 24-20 = 4.
Success!

The correct answer is C.

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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
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:

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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