Question

A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?

Answer 1

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

Explanation:

Let the number of mangoes bought by the grocery store be n. Also let the number of mango sold for $3 in one stack be x and the number of mango sold for $6 in the second stack be y.

Therefore:

x + y = z (1)

Also, the mangoes was sold at break even price, that is the cost of the mango and the price it was sold for was the same. Therefore:

Cost of buying = Price it was sold for

The cost of the mango = 5z and the price it was sold for = 3x + 6y

3x + 6y = 5z (2)

Substituting z = x + y in equation 1

3x + 6y = 5(x + y)

3x + 6y = 5x + 5y

6y - 5y = 5x - 3x

y = 2x

x / y = 1/ 2 = 1 : 2

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2