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Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo

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Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo [#permalink]

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New post 17 Oct 2016, 22:25
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Aunt Maura spends $12 on mangoes at a local merchant. If Aunt Maura bought the mangoes at a shopping center instead, she could purchase an extra pound of mangoes for the same amount of money. The mangoes are $1 cheaper per pound at the shopping center than at the local merchant. What is the price per pound of mangoes at the local merchant?

a) $3
b) $4
c) $5
d) $6
e) $7

Please assist with above problem.
[Reveal] Spoiler: OA
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Re: Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo [#permalink]

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P*Q = 12 and (P-1)(Q+1)= 12 --> Q= P-1 --> P(P-1)=12 --> P = 4
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Re: Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo [#permalink]

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New post 18 Oct 2016, 00:06
yennguyen wrote:
P*Q = 12 and (P-1)(Q+1)= 12 --> Q= P-1 --> P(P-1)=12 --> P = 4


Thanks for your explanation! Could you kindly explain how Q=P-1 came about?

I solve this question through testing the numbers and I want to understand your approach! :)
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Re: Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo [#permalink]

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alanforde800Maximus wrote:
Aunt Maura spends $12 on mangoes at a local merchant. If Aunt Maura bought the mangoes at a shopping center instead, she could purchase an extra pound of mangoes for the same amount of money. The mangoes are $1 cheaper per pound at the shopping center than at the local merchant. What is the price per pound of mangoes at the local merchant?

a) $3
b) $4
c) $5
d) $6
e) $7

Please assist with above problem.


The following things must ring the bells about the relationship between the Prices in hopping center & local merchant.

1. Aunt Maura spends $12 on mangoes at a local merchant
2. The mangoes are $1 cheaper per pound at the shopping center than at the local merchant.
3. She could purchase an extra pound of mangoes for the same amount of money.

12 = 3 * 4 ( as we know )

So, We can find the value for price per pound of mangoes at the local merchant as $4

Answer will be (B) $ 4 ..
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Re: Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo [#permalink]

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New post 18 Oct 2016, 23:48
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Hi Mimster, (P-1)(Q+1)=12 --> PQ + P-Q-1=12 and PQ = 12 --> Q = P-1. That's how it is. :D
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Re: Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo [#permalink]

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Cost at local store = x

Qty bought at local store = y

x*y = 12

Price at shopping center = x-1

Qty at shopping center = y+1

(x-1)*(y+1) = 12

xy + x -y -1 =12

we know xy =12

12 + x -y -1 =12

x - y = 1

x = y + 1

(y+1)y = 12 or x(x-1) = 12

Solving the quardratic will give x = 4

Option B
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Re: Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo [#permalink]

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New post 08 Dec 2017, 13:18
alanforde800Maximus wrote:
Aunt Maura spends $12 on mangoes at a local merchant. If Aunt Maura bought the mangoes at a shopping center instead, she could purchase an extra pound of mangoes for the same amount of money. The mangoes are $1 cheaper per pound at the shopping center than at the local merchant. What is the price per pound of mangoes at the local merchant?

a) $3
b) $4
c) $5
d) $6
e) $7


We are given that Aunt Maura spends $12 on mangoes at a local merchant and that if Aunt Maura bought the mangoes at a shopping center instead, she could purchase an extra pound of mangoes for the same amount of money. We are also given that the price per pound of mangoes at the shopping center is $1 cheaper than the price at the local merchant.

We can let p = the price per pound of mangoes at the local merchant and q = the number of pounds of mangoes purchased at the local merchant.

Thus, the number of pounds of mangoes purchased at the shopping center = q + 1 and the price per pound at the shopping center = p - 1.

Thus, we have two equations:

pq = 12

AND

(p - 1)(q + 1) = 12

pq - q + p - 1 = 12

Since 12/p = q, we can substitute 12/p for q in the equation pq - q + p - 1 = 12 and have:

p(12/p) - 12/p + p = 13

12 - 12/p + p = 13

Multiplying the entire equation by p gives us:

12p - 12 + p^2 = 13p

p^2 - p - 12 = 0

(p - 4)(p + 3) = 0

p = 4 or p = -3

Since p must be positive, p = 4.

Answer: B
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Re: Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo [#permalink]

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New post 21 Jan 2018, 13:25
Hi All,

This question has a number of built-in patterns that you can take advantage of. First, the answer choices are small integers, so you can TEST THE ANSWERS. Second, the numbers involved are also all integers... Maura bought $12 worth of mangoes at a merchant, but the mangos are $1 cheaper per pound at the shopping center - and at that price she could purchase 1 extra pound of mangos for $12..

From the answer choices, we can see that the total cost per pound at the merchant must ALSO be an integer... almost certainly one that divides evenly into $12. So we need two integers, one for each of the two prices... that BOTH divide into $12 AND that differ by $1. That can ONLY be $3 and $4. Now we just have to double-check to make sure that we're answering the question that is asked...

$12 spent at the merchant (where mangoes are $4 a pound) = 3 pounds
$12 spent at the center (where mangoes are $3 a pound) = 4 pounds

This matches perfectly. The question asks for the price per pound at the merchant....

Final Answer:
[Reveal] Spoiler:
B


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Re: Aunt Maura spends $12 on mangoes at a local merchant. If Aunt maura bo   [#permalink] 21 Jan 2018, 13:25
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