Question

A company offers a nut mixture with 8 peanuts for every 7 almonds. The company changes the mixture to have 3 peanuts for every 1 almond, but the number of nuts per container does not change. How many nuts are in the smallest possible container?

Answer 1

The smallest possible container size will contain a total of 11 nuts (3 peanuts + 8 almonds).

Step-by-step explanation:

To find the smallest possible container size, we need to determine the total number of nuts in the mixture before and after the change. Let's assume the smallest possible number of nuts in the container is 1. We can set up two equations to represent the number of peanuts and almonds in the original mixture:

Equation 1: 8x = number of peanuts (x represents the smallest possible number of peanuts)

Equation 2: 7x = number of almonds (x represents the smallest possible number of almonds)

Solving these equations, we find that the smallest possible number of peanuts is 7 and the smallest possible number of almonds is 8.

After the change, the new ratio is 3 peanuts for every 1 almond. Let's set up two new equations:

Equation 3: 3y = number of peanuts in the new mixture (y represents the smallest possible number of peanuts in the new mixture)

Equation 4: y = number of almonds in the new mixture (the smallest possible number of almonds will be the same as the number of almonds in the original mixture)

Solving these equations, we find that the smallest possible number of peanuts in the new mixture is 3 and the smallest possible number of almonds in the new mixture is 8. Therefore, the smallest possible container size will contain a total of 11 nuts (3 peanuts + 8 almonds).