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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