Problem Solving

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?

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!

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.

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.

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.