Question

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?

Answer 1

Price per pound of mangos at the local merchant = 4

Step-by-step 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.