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

Price per pound of mangos at the local merchant = 4

Explanation:

We are going to propose a system of 2 equations with 2 unknowns

a) P * Q = 12

b) (P - 1) * (Q + 1) = 12

Where

P is Price and Q is Quantity

and

Equation a) represents local merchant and Equation b) represents the shopping center.

Now we use the substitution method to solve this:

First we clear quantity from equation a)

a) P * Q = 12

Q = 12 / P

Then we replace it in equation b)

b) (P - 1) * (Q + 1) = 12

(P - 1) * ((12 / P) + 1) = 12

And now we solve the resulting equation

(P - 1) * ((12 / P) + 1) = 12

(12P / P) + P - (12 / P) - 1 = 12

12 + P - (12 / P) - 1 = 12

P - (12 / P) = 12 - 12 + 1

P - (12 / P) = 1

(12 / P) = - 1 + P

12 = P (-1 + P)

12 = - P + P ^ 2

0 = - P + P ^ 2 - 12

Calculating the routs

x1 = - 3

x2 = 4

We choose the positive one, with means the price is 4.

So the price is 4 and the quantity 3 in the local merchant. In the shopping center the price is 3 and the quantity 4. Both gives the total amount of 12 dollars.